document.write( "Question 183214: \"what are the values of a and c in the trinomial square ax^2+12x+c if a is not 1 and c is greater than a?\" \n" ); document.write( "

Algebra.Com's Answer #137561 by josmiceli(19441) $\"\"$ $\"About$

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If $\"ax%5E2+%2B+12x+%2B+c\"$ is a square, it can be expressed as
\n" ); document.write( "(1) $\"%28sqrt%28a%29%2Ax+%2B+sqrt%28c%29%29%5E2\"$
\n" ); document.write( "performing the square, I get
\n" ); document.write( " $\"ax%5E2+%2B+2%2Asqrt%28a%29%2Asqrt%28c%29%2Ax+%2B+c\"$
\n" ); document.write( " $\"ax%5E2+%2B+sqrt%284ac%29%2Ax+%2B+c\"$
\n" ); document.write( "Comparing this with
\n" ); document.write( " $\"ax%5E2+%2B+12x+%2B+c\"$
\n" ); document.write( " $\"12+=+sqrt%284ac%29\"$
\n" ); document.write( "square both sides
\n" ); document.write( " $\"144+=+4ac\"$
\n" ); document.write( " $\"ac+=+36\"$
\n" ); document.write( " $\"c+=+36%2Fa\"$
\n" ); document.write( " $\"c\"$ should be a perfect square
\n" ); document.write( "If $\"c+%3E+a\"$ ,
\n" ); document.write( " $\"a+=+4\"$ and
\n" ); document.write( " $\"9+=+36%2F4\"$ is the only possibility
\n" ); document.write( " $\"ax%5E2+%2B+12x+%2B+c+=+4x%5E2+%2B+12x+%2B+9\"$ answer \n" ); document.write( "

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