x^2 + 10x = - 5
To complete the square, we need to add a constant on the
left side that makes the expression on the right a perfect square trinomial. We
need to add the same value on the right side to keep the equation equal. So,
x^2 + 10x + a = -5 + a
where a is the square of one-half the coefficient of x, therefore:
a = (10 / 2)^2 = 25
x^2 + 10x + 25 = -5 + 25
(x + 5)^2 = 20
Taking the square root of both sides:
x + 5 = ± 4.47
x = -5 ± 4.47
x = -9.47, -0.53
