document.write( "Question 987707: Find the value(s) of k that makes x^2 + (k+5)x + (5k+1) a perfect square trinomial. \n" ); document.write( "

Algebra.Com's Answer #608476 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Subtract x² from both sides:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Equate the coefficients of x on each side\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Equate the constant terms on each side:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we have this system of two equations in two unknowns:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Solve the first equation for k\r\n" );
document.write( "\r\n" );
document.write( "k = 2A-5\r\n" );
document.write( "\r\n" );
document.write( "Substitute in the second:\r\n" );
document.write( "\r\n" );
document.write( "5(2A-5)+1 = A²\r\n" );
document.write( "\r\n" );
document.write( "10A - 25 + 1 = A²\r\n" );
document.write( "\r\n" );
document.write( "0 = A² - 10A + 24\r\n" );
document.write( "\r\n" );
document.write( "0 = (A - 6)(A - 4)\r\n" );
document.write( "\r\n" );
document.write( "A - 6 = 0;  A - 4 = 0\r\n" );
document.write( "    A = 6;      A = 4\r\n" );
document.write( "\r\n" );
document.write( "k = 2A-5;     k = 2A-5\r\n" );
document.write( "k = 2(6)-5;   k = 2(4)-5\r\n" );
document.write( "k = 12-5;     k = 8-5\r\n" );
document.write( "k = 3         k = 7\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );