document.write( "Question 549677: What is the proof of the quadratic formula?
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Algebra.Com's Answer #357939 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Start with the general quadratic equation:\r\n" );
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document.write( " Ax² + Bx + C = 0\r\n" );
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document.write( "Subtract C from both sides\r\n" );
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document.write( "     Ax² + Bx = -C\r\n" );
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document.write( "Divide through by A\r\n" );
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document.write( "    x² + x = \r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "     x² + x = \r\n" );
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document.write( "                                   Multiply the coefficient of x by :   = \r\n" );
document.write( "                                   Square .   = \r\n" );
document.write( "                                   Add  to both sides:\r\n" );
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document.write( "x² + x +  =  - \r\n" );
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document.write( "Factor the left side and get LCD of 4A² on the right\r\n" );
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document.write( "(x + )(x + ) =  - \r\n" );
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document.write( "Write left side as the square of a binomial.  Multiply fractions on far right\r\n" );
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document.write( "(x + )² =  - \r\n" );
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document.write( "Combine fractions on the right over the LCD\r\n" );
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document.write( "(x + )² =  \r\n" );
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document.write( "Use the principle of square roots:\r\n" );
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document.write( "x +  = \r\n" );
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document.write( "Take square roots of top and bottom on the right:\r\n" );
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document.write( "x +  = \r\n" );
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document.write( "x +  = \r\n" );
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document.write( "Add  to both sides:\r\n" );
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document.write( "               x =  ± \r\n" );
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document.write( "Combine the fractions on the right over 2A\r\n" );
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document.write( "               x = \r\n" );
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document.write( "Edwin

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