You can "complete the square" by adding 13 to both sides of the equation.
x^2 + 6x - 4 = 0
x^2 + 6x + 9 = 13 (you need to recognize that you want to end with a constant of (6/2)^2 = 9 on the left side. Starting from -4, this means you add 13.)
(x+3)^2 = 13 (rewrite as a square. This is the form we were trying to get to.)
Now, take the square root and subtract 3
x+3 = ±√13
x = -3 ± √13 _____
√13 ≈ 3.60555, so x is approximately -6.60555, +0.60555.
x^2 + 6x + 9 = 13 (you need to recognize that you want to end with a constant of (6/2)^2 = 9 on the left side. Starting from -4, this means you add 13.)
(x+3)^2 = 13 (rewrite as a square. This is the form we were trying to get to.)
Now, take the square root and subtract 3
x+3 = ±√13
x = -3 ± √13 _____
√13 ≈ 3.60555, so x is approximately -6.60555, +0.60555.
