document.write( "Question 1209150: Find all real values of s such that x^2 + sx + 144 - 6x + 3x^2 is the square of a binomial. \n" ); document.write( "

Algebra.Com's Answer #847731 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( " $\"x%5E2+%2B+sx+%2B+144+-+6x+%2B+3x%5E2\"$ = $\"4x%5E2%2B%28s-6%29x%2B144\"$

\n" ); document.write( "In the simplified polynomial, the leading term is $\"4x%5E2\"$ , so the leading term of the square root is $\"sqrt%284x%5E2%29\"$ = $\"2x\"$ .

\n" ); document.write( "The constant term of the simplified polynomial is 144, so the constant term of the square root is $\"sqrt%28144%29\"$ = $\"12\"$ .

\n" ); document.write( "So the possible square root polynomials are $\"2x%2B12\"$ and $\"2x-12\"$ .

\n" ); document.write( " $\"%282x%2B12%29%5E2+=+4x%5E2%2B48x%2B144\"$ so for one solution we have

\n" ); document.write( " $\"s-6=48\"$ --> $\"s=54\"$

\n" ); document.write( " $\"%282x-12%29%5E2+=+4x%5E2-48x%2B144\"$ so for a second solution we have

\n" ); document.write( " $\"s-6=-48\"$ --> $\"s=-42\"$

\n" ); document.write( "ANSWERS: s=54 and s=-42

\n" ); document.write( " \n" ); document.write( "

\n" );