A3.4: Solve complicated quadratic equations Complicated Quadratic 1 Solve the following quadratic equation:

\( (3x-2)^2=121 \)

If there are multiple rational answers, put them in braces {} separated by commas.  If there are multiple irrational and/or imaginary answers, use the +/- sign.

]]> 1.0000000 0.3333333 0 0 -3,133]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close="}"><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mfrac><mn>13</mn><mn>3</mn></mfrac></mrow></mfenced></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Complicated Quadratic 10 Solve the following quadratic equation:

\( \frac{x^2+1}{x+2}=\frac{x}{3}+\frac{5}{x+2} \)

If there are multiple rational answers, put them in braces {} separated by commas.  If there are multiple irrational and/or imaginary answers, use the +/- sign.

]]> 1.0000000 0.3333333 0 0 3 <question><correctAnswers><correctAnswer>3</correctAnswer></correctAnswers><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Complicated Quadratic 11 Solve the following quadratic equation:

\( \frac{x+2}{x^2-x-6}=3-\frac{4}{x-3} \)

If there are multiple rational answers, put them in braces {} separated by commas.  If there are multiple irrational and/or imaginary answers, use the +/- sign.

]]> 1.0000000 0.3333333 0 0 143]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>14</mn><mn>3</mn></mfrac></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Complicated Quadratic 12 Solve the following quadratic equation:

\( 2 \sqrt{x}=x-8 \)

If there are multiple rational answers, put them in braces {} separated by commas.  If there are multiple irrational and/or imaginary answers, use the +/- sign.

]]> 1.0000000 0.3333333 0 0 16 <question><correctAnswers><correctAnswer>16</correctAnswer></correctAnswers><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Complicated Quadratic 13 Solve the following quadratic equation:

\( \sqrt{2x+5}=x+1 \)

If there are multiple rational answers, put them in braces {} separated by commas.  If there are multiple irrational and/or imaginary answers, use the +/- sign.

]]> 1.0000000 0.3333333 0 0 2 <question><correctAnswers><correctAnswer>2</correctAnswer></correctAnswers><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Complicated Quadratic 14 Solve the following quadratic equation:

\( \sqrt{2}x^2-5x+ \sqrt{8} =0 \)

If there are multiple rational answers, put them in braces {} separated by commas.  If there are multiple irrational and/or imaginary answers, use the +/- sign.

]]> 1.0000000 0.3333333 0 0 22,22]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close="}"><mrow><mn>2</mn><msqrt><mn>2</mn></msqrt><mo>,</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></mrow></mfenced></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Complicated Quadratic 15 Solve the following quadratic equation:

\( 4x^2-2 \sqrt{5}x-1=0 \)

If there are multiple rational answers, put them in braces {} separated by commas.  If there are multiple irrational and/or imaginary answers, use the +/- sign.

]]> 1.0000000 0.3333333 0 0 5±34]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msqrt><mn>5</mn></msqrt><mo>&#xB1;</mo><mn>3</mn></mrow><mn>4</mn></mfrac></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Complicated Quadratic 2 Solve the following quadratic equation:

\( 4x=1+15x^2 \)

If there are multiple rational answers, put them in braces {} separated by commas.  If there are multiple irrational and/or imaginary answers, use the +/- sign.

]]> 1.0000000 0.3333333 0 0 2±i1115]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>&#xB1;</mo><mi mathvariant="normal">i</mi><msqrt><mn>11</mn></msqrt></mrow><mn>15</mn></mfrac></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Complicated Quadratic 3 Solve the following quadratic equation:

\( (4x+4)^2=16 \)

If there are multiple rational answers, put them in braces {} separated by commas.  If there are multiple irrational and/or imaginary answers, use the +/- sign.

]]> 1.0000000 0.3333333 0 0 -1±i]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>&#xB1;</mo><mi mathvariant="normal">i</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Complicated Quadratic 4 Solve the following quadratic equation:

\( (4x+7)(x-1)=2(x-1) \)

If there are multiple rational answers, put them in braces {} separated by commas.  If there are multiple irrational and/or imaginary answers, use the +/- sign.

]]> 1.0000000 0.3333333 0 0 1,-54]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close="}"><mrow><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>5</mn><mn>4</mn></mfrac></mrow></mfenced></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Complicated Quadratic 5 Solve the following quadratic equation:

\( (2x+1)(4x-3)=3(4x-3)^2 \)

If there are multiple rational answers, put them in braces {} separated by commas.  If there are multiple irrational and/or imaginary answers, use the +/- sign.

]]> 1.0000000 0.3333333 0 0 1,34]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close="}"><mrow><mn>1</mn><mo>,</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></mrow></mfenced></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Complicated Quadratic 6 Solve the following quadratic equation:

\( 2x(4x-1)=x(1-4x) \)

If there are multiple rational answers, put them in braces {} separated by commas.  If there are multiple irrational and/or imaginary answers, use the +/- sign.

]]> 1.0000000 0.3333333 0 0 0,14]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close="}"><mrow><mn>0</mn><mo>,</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></mrow></mfenced></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Complicated Quadratic 7 Solve the following quadratic equation:

\( 3(2x-3)^2=4x(3-2x) \)

If there are multiple rational answers, put them in braces {} separated by commas.  If there are multiple irrational and/or imaginary answers, use the +/- sign.

]]> 1.0000000 0.3333333 0 0 910,32]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close="}"><mrow><mfrac><mn>9</mn><mn>10</mn></mfrac><mo>,</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mrow></mfenced></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Complicated Quadratic 8 Solve the following quadratic equation:

\( \frac{x+3}{x-3}+\frac{x-3}{x+3}=\frac{18-6x}{x^2-9} \)

If there are multiple rational answers, put them in braces {} separated by commas.  If there are multiple irrational and/or imaginary answers, use the +/- sign.

]]> 1.0000000 0.3333333 0 0 0 <question><correctAnswers><correctAnswer>0</correctAnswer></correctAnswers><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Complicated Quadratic 9 Solve the following quadratic equation:

\( \frac{x}{x-1}-\frac{x}{x+1}=\frac{2}{x^2-1} \)

If there are multiple rational answers, put them in braces {} separated by commas.  If there are multiple irrational and/or imaginary answers, use the +/- sign.

]]> 1.0000000 0.3333333 0 0 No Solution]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mi>o</mi><mo>&#xA0;</mo><mi>S</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">B7</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>