document.write( "Question 332146: Please help me solve the quadratic equation -9x + 24x -16 = 0 \n" ); document.write( "

Algebra.Com's Answer #238055 by Edwin McCravy(20056) $\"\"$ $\"About$

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$\"-9x%5E2+%2B+24x+-16+=+0\"$
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document.write( "Since the leading term (tho one with the largest\r\n" );
document.write( "exponent is negative, we multiply every term by -1\r\n" );
document.write( "so the leading term will be positive.  So we\r\n" );
document.write( "multiply through by -1.  Thart changes all the signs:\r\n" );
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document.write( "Both the first term and the last term are perfect squares.\r\n" );
document.write( "The first term  is a perfect square, since it\r\n" );
document.write( "can be written as .  And the last term  can\r\n" );
document.write( "be written .\r\n" );
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document.write( "So the whole trinomial is a candidate for being a perfect square.\r\n" );
document.write( "It may not be but we need to check to find out if it is actually\r\n" );
document.write( "a perfect square.  Here is the test:\r\n" );
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document.write( "Multiply the square roots of the first and last terms on the left.\r\n" );
document.write( "Then double what you get.  If you get the same thing as the middle \r\n" );
document.write( "term, or the middle term with the opposite sign, then it is a perfect\r\n" );
document.write( "square, and factors as \r\n" );
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document.write( "(Square root of first term, sign of muddle term, Square root of last term)²\r\n" );
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document.write( "The square roots are 3x and 4.  Multiply them.  Get 12x.\r\n" );
document.write( "Then double that and get 24x.  That is the same thing as the middle term \r\n" );
document.write( "-24x, with the opposite sign, so it is a perfect square, and factors as\r\n" );
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document.write( "So there is only one solution, found by setting\r\n" );
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document.write( "Edwin

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