document.write( "Question 783793: What do you think it means when A is not 1 when we attempt to complete the square? For example, 5x squared + 25x + 10 = 45 what A represents or B tell me how to make A = 1 \n" ); document.write( "

Algebra.Com's Answer #476915 by josgarithmetic(39630) $\"\"$ $\"About$

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What is the meaning of A and B?
\n" ); document.write( "You give an equation and you give a mention about A and B but nowhere indicate what these two variables mean. \r
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\n" ); document.write( "\n" ); document.write( "A best-guess is that the A and B are part of the more general, $\"Ax%5E2%2BBx%2BC=0+\"$ quadratic equation. You do NOT make A=1. In your given equation, $\"5x%5E2%2B25x%2B10=45\"$ , A=5. Also, B=25. You can Complete the Square if you like, but A=5 and B=25 whatever you do. \r
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\n" ); document.write( "\n" ); document.write( "What you want when you Complete the Square is to factorize the quadratic expression in your equation which effectively gives you a quadratic expression in which the coefficient on $\"x%5E2\"$ will be 1. Your left side would go like this:\r
\n" ); document.write( "\n" ); document.write( " $\"5x%5E2%2B25x%2B10\"$
\n" ); document.write( " $\"5%28x%5E2%2B5x%2B2%29\"$
\n" ); document.write( "and you would determine that the square term to add & subtract, or to just add to both sides of the equation, would be $\"%285%2F2%29%5E2=25%2F4\"$ , which corresponds to the more general $\"%28B%2F2%29%5E2=%281%2F4%29B%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note, what I should also say,
\n" ); document.write( "WITHIN the quadratic factor, $\"x%5E2%2B5x%2B2\"$ , A=1 and B=5, but this is only if we first ignore labeling the coefficients in the original equation and focus only on the coefficients in the quadratic factor. To say that A=1 and A=5 is really a BAD IDEA. \n" ); document.write( "

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