Algebra 2 question - help

What number do I add to both sides of this equation to factor it using square roots?

x^2 + 6x = -2

I think you are talking about "completing the square". If so, add the square of 1/2 the x coefficient, (6/2)² = 9

x² + 6x + 9 = 7
(x+3)² = 7

I think what you mean is completing the square.

b = 6
b/2 = 6/2 = 3
(b/2)^2 = 3^2 = 9

x^2 + 6x + 9 = -2 + 9
(x + 3)^2 = 7
x + 3 = +/- sqrt(7)
x = -3 +/- sqrt(7)

9.
and next time use this expression to find the number you need: (b/2)^2
when b is the second term of the quadratic. (in this case, b=6)

9. The equation is (b/2)^2. 6/2=3, 3^2=9.

... x^2 + 6x = -2
or x^2 + 2(x)(3) = -2
or x^2 + 2(x)(3) + (3)^2 = -2 + (3)^2
or (x + 3)^2 = -2 + (3)^2