document.write( "Question 1184674: Express 6x-x^2 in the form a-(x+b)^2 \n" ); document.write( "
Algebra.Com's Answer #815304 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Set them identically \"≡\" (not conditionally \"=\") equal.\r\n" );
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document.write( "6x-x2 ≡ a-(x+b)2\r\n" );
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document.write( "6x-x2 ≡ a-(x2+2bx+b2)\r\n" );
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document.write( "6x-x2 ≡ a-x2-2bx-b2)\r\n" );
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document.write( "Add x2 to both sides:\r\n" );
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document.write( "6x ≡ a-2bx-b2\r\n" );
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document.write( "Now here is where we can do something in identity equations \r\n" );
document.write( "that we cannot do in a conditional equations.  That is, in \r\n" );
document.write( "identity equations we can equate coefficients of like powers \r\n" );
document.write( "of x (as well as constant terms).\r\n" );
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document.write( "The coefficient of x on the left is 6 and the coefficient\r\n" );
document.write( "of x on the right is -2b, and since this is an identity\r\n" );
document.write( "equation and not a conditional equation, we can set 6 and\r\n" );
document.write( "-2b (conditionally) equal to each other:\r\n" );
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document.write( " 6 = -2b\r\n" );
document.write( "-3 = b\r\n" );
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document.write( "Now we substitute -3 for b\r\n" );
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document.write( "6x ≡ a-2bx-b2\r\n" );
document.write( "6x ≡ a-2(-3)x-(-3)2\r\n" );
document.write( "6x ≡ a+6x-9\r\n" );
document.write( " 9 ≡ a\r\n" );
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document.write( "Now let's check to see if we have an identity equation by \r\n" );
document.write( "substituting:\r\n" );
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document.write( "6x-x2 ≡ a-(x+b)2\r\n" );
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document.write( "6x-x2 ≡ 9-[x+(-3)]2\r\n" );
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document.write( "6x-x2 ≡ 9-(x-3)2\r\n" );
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document.write( "6x-x2 ≡ 9-(x2-6x+9)\r\n" );
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document.write( "6x-x2 ≡ 9-x2+6x-9\r\n" );
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document.write( "6x-x2 ≡ -x2+6x\r\n" );
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document.write( "6x-x2 ≡ 6x-x2\r\n" );
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document.write( "Yep, both sides are identical!\r\n" );
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document.write( "Edwin
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