document.write( "Question 818423: solving equations by completing the square.\r
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\n" ); document.write( "\n" ); document.write( "I can't seem to come up with two factors that work. \n" ); document.write( "

Algebra.Com's Answer #492551 by Edwin McCravy(20055) $\"\"$ $\"About$

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solving equations by completing the square.
\n" ); document.write( " p^2+16p-22=0
\n" ); document.write( " I can't seem to come up with two factors that work.
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document.write( "Of course you can't seem to come up with two factors\r\n" );
document.write( "that work.  There ARE NONE!  :)\r\n" );
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document.write( "That's why they told you to COMPLETE THE SQUARE instead.\r\n" );
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document.write( "Completing the square is what you have to do when the\r\n" );
document.write( "quadratic cannot be factored.\r\n" );
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document.write( "p²+16p-22 = 0\r\n" );
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document.write( "Isolate the variable terms by adding 22 to both sides:\r\n" );
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document.write( "   p²+16p = 22\r\n" );
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document.write( "Multiply the coefficient of p, which is 16, by  getting\r\n" );
document.write( "16· = 8.  Then square 8, getting 64.  Add 64 to both sides \r\n" );
document.write( "of the equation.\r\n" );
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document.write( "p²+16p+64 = 22+64\r\n" );
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document.write( "Now the left side will factor.  Combine the numbers on the right:\r\n" );
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document.write( "(p+8)(p+8) = 86\r\n" );
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document.write( "Note that the left side has factored a special way.  Both factors are\r\n" );
document.write( "the same, so we can write:\r\n" );
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document.write( "    (p+8)² = 86\r\n" );
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document.write( "Now we take square roots of both sides:\r\n" );
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document.write( "   √(p+8)² = ±√86\r\n" );
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document.write( "       p+8 = ±√86\r\n" );
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document.write( "         p = -8±√86\r\n" );
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document.write( "So there are two solutions:\r\n" );
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document.write( "Using the +:   p = -8+√86\r\n" );
document.write( " which is approximately 1.273618495\r\n" );
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document.write( "Using the -:   p = -8-√86 \r\n" );
document.write( "which is approximately -17.2736185\r\n" );
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document.write( "Edwin

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