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<title>Solving Quadratic Equations</title>
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<h2 id="heading">Solving Quadratic Equations</h2>
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&#160;&#160;&#160;If &#160;<math><mstyle mathcolor="blue"><mstyle><mi>a</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle><mo stretchy="false">+</mo><mstyle><mi>b</mi><mi>x</mi></mstyle><mo stretchy="false">+</mo><mstyle><mi>c</mi></mstyle></mstyle></math> = 0, then&#160;<math><mstyle mathcolor="blue"><mi>x</mi></mstyle></math> = &#160;<math><mstyle mathcolor="blue"><mfrac><mrow><mi>-b</mi><mo stretchy="true">&#x00B1;</mo><msqrt><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false">-</mo><mi>4ac</mi></msqrt></mrow><mrow><mi>2a</mi></mrow></mfrac></mstyle></math><br/><br/>So, if &#160;<math><mstyle mathcolor="blue"><mi></mi><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false">-</mo><mn>12</mn><mi>x</mi><mo stretchy="false">+</mo><mn>20</mn></mstyle></math> = 0, then <br/><br/>&#160; &#160;&#160;&#160;<math><mstyle mathcolor="blue"><mi>x</mi></mstyle></math> = &#160;<math><mstyle mathcolor="blue"><mfrac><mrow><mo stretchy="false">-</mo><mo stretchy="false">(</mo><mn>-12</mn><mo stretchy="false">)</mo><mo stretchy="true">&#x00B1;</mo><msqrt><msup><mrow><mo stretchy="false">(</mo><mi>-12</mi><mo stretchy="false">)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false">-</mo><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>20</mn><mo stretchy="false">)</mo></msqrt></mrow><mrow><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mfrac></mstyle></math><br/><br/>or,&#160;<math><mstyle mathcolor="blue"><mi>x</mi></mstyle></math> = &#160;<math><mstyle mathcolor="blue"><mfrac><mrow><mi>12</mi><mo stretchy="true">&#x00B1;</mo><msqrt><mn>144</mn><mo stretchy="false">-</mo><mn>80</mn></msqrt></mrow><mrow><mi>2</mi></mrow></mfrac></mstyle></math><br/><br/>or,&#160;<math><mstyle mathcolor="blue"><mi>x</mi></mstyle></math> = &#160;<math><mstyle mathcolor="blue"><mfrac><mrow><mi>12</mi><mo stretchy="true">&#x00B1;</mo><msqrt><mn>64</mn></msqrt></mrow><mrow><mi>2</mi></mrow></mfrac></mstyle></math><br/><br/>or,&#160;<math><mstyle mathcolor="blue"><mi>x</mi></mstyle></math> = &#160;<math><mstyle mathcolor="blue"><mfrac><mrow><mi>12</mi><mo stretchy="true">&#x00B1;</mo><mn>8</mn></mrow><mrow><mi>2</mi></mrow></mfrac></mstyle></math><br/><br/>or, &#160;<math><mstyle mathcolor="blue"><mi>x</mi></mstyle></math> = &#160;<math><mstyle mathcolor="blue"><mfrac><mrow><mn>20</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> or, &#160;<math><mstyle mathcolor="blue"><mi>x</mi></mstyle></math> = &#160;<math><mstyle mathcolor="blue"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math><br/><br/>or, &#160;<math><mstyle mathcolor="blue"><mi>x</mi></mstyle></math> = &#160;<math><mstyle mathcolor="blue"><mn>10</mn></mstyle></math> or, &#160;<math><mstyle mathcolor="blue"><mi>x</mi></mstyle></math> = &#160;<math><mstyle mathcolor="blue"><mn>2</mn></mstyle></math>
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Some steps shown in the examples may not be necessary. 
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If you have any question or suggestion or comment, please email 
<a href="mailto:dpurohit@jds.com">me</a>

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<hr/>Copyright &#169; Dayal D. Purohit, Ph.D.(Mathematics)
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