It seems like you are trying to complete the square for the equation x^2 + 6x = -1. Let me guide you through the process.
To complete the square, we aim to rewrite the left side of the equation as a perfect square trinomial. The general steps are as follows:
1. Move the constant term (-1 in this case) to the right side of the equation:
x^2 + 6x + 1 = 0
2. Take half of the coefficient of the x-term (6), square it, and add it to both sides of the equation:
x^2 + 6x + (6/2)^2 = 1 + (6/2)^2
x^2 + 6x + 9 = 1 + 9
x^2 + 6x + 9 = 10
Now we have a perfect square trinomial on the left side, which can be factored into the square of a binomial:
(x + 3)^2 = 10
To solve for x, we can take the square root of both sides:
√((x + 3)^2) = ±√10
Simplifying further:
x + 3 = ±√10
Finally, isolate x by subtracting 3 from both sides:
x = -3 ± √10
So the solution to the original equation x^2 + 6x = -1 is x = -3 ± √10.