Question 987707
<pre>
{{{x^2 + (k+5)x + (5k+1)}}}{{{""=""}}}{{{(x+A)^2}}}

{{{x^2 + (k+5)x + (5k+1)}}}{{{""=""}}}{{{(x+A)(x+A)}}}

{{{x^2 + (k+5)x + (5k+1)}}}{{{""=""}}}{{{x^2+2Ax+A^2}}}

Subtract x² from both sides:

{{{(k+5)x + (5k+1)}}}{{{""=""}}}{{{2Ax+A^2}}}

Equate the coefficients of x on each side

{{{(k+5)}}}{{{""=""}}}{{{2A}}}

Equate the constant terms on each side:

{{{5k+1}}}{{{""=""}}}{{{A^2}}}

So we have this system of two equations in two unknowns:

{{{system(k+5=2A,5k+1=A^2)}}}

Solve the first equation for k

k = 2A-5

Substitute in the second:

5(2A-5)+1 = A²

10A - 25 + 1 = A²

0 = A² - 10A + 24

0 = (A - 6)(A - 4)

A - 6 = 0;  A - 4 = 0
    A = 6;      A = 4

k = 2A-5;     k = 2A-5
k = 2(6)-5;   k = 2(4)-5
k = 12-5;     k = 8-5
k = 3         k = 7

Edwin</pre>