Question 196540
{{{x^2 + 8x + 13 = 0}}}
{{{x^2 + 8x = -13}}}
{{{x^2 + 8x + (8/2)^2 = -13 + (8/2)^2}}}
{{{x^2 + 8x + 16 = -13 + 16}}}
The left side is a perfect square
{{{(x + 4)^2 = 3}}}
Take the square root of both sides
{{{x + 4 = sqrt(3)}}}
{{{x = 14 + sqrt(3)}}}
and
{{{x + 4 = -sqrt(3)}}}
{{{x = -4 - sqrt(3)}}}
I'll check the 2nd result
{{{x^2 + 8x + 13 = 0}}}
{{{(-4 - sqrt(3))^2 + 8*(-4 -sqrt(3)) + 13 = 0}}}
{{{16 + 8*sqrt(3) + 3 - 32 - 8*sqrt(3) + 13 = 0}}}
{{{16 + 3 - 32 + 13 = 0}}}
{{{0 = 0}}}
OK