document.write( "Question 628946: If x^2+kx+64=(x+r)^2 and r>0, what is the value of k? \n" ); document.write( "

Algebra.Com's Answer #395920 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
We can use the $\"%28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2\"$ for this problem. It gives us a pattern for every square of a binomial. So for
\n" ); document.write( " $\"x%5E2%2Bkx%2B64\"$ to be equal to $\"%28x%2Br%29%5E2\"$ , then it must fit this pattern!

\n" ); document.write( "Let's look at $\"a%5E2%2B2ab%2Bb%5E2\"$ term by term:
\n" ); document.write( "The first term of $\"a%5E2%2B2ab%2Bb%5E2\"$ is $\"a%5E2\"$ which is a perfect square. The first term of $\"x%5E2%2Bkx%2B64\"$ is $\"x%5E2\"$ , also a perfect square. So far we have matched the pattern with the \"a\" being \"x\".
\n" ); document.write( "The last term of $\"a%5E2%2B2ab%2Bb%5E2\"$ is $\"b%5E2\"$ which is also a perfect square. The last term of $\"x%5E2%2Bkx%2B64\"$ is 64, a perfect square (the square of 8). So far we have matched the pattern with the \"a\" being \"x\" and the \"b\" being \"8\"
\n" ); document.write( "The middle term of $\"a%5E2%2B2ab%2Bb%5E2\"$ is 2ab, the product of 2, the \"a\" and the \"b\". In order for $\"x%5E2%2Bkx%2B64\"$ to match the pattern of $\"a%5E2%2B2ab%2Bb%5E2\"$ completely, its middle term, kx, must be the product of 2, the \"a\" (which is \"x\") and the \"b\" (which is \"8\") So
\n" ); document.write( "kx = 2*x*8
\n" ); document.write( "which simplifies to:
\n" ); document.write( "kx = 16x
\n" ); document.write( "So k = 16. \n" ); document.write( "

\n" );