First move the 9 to the right side by subtracting 9 from both sides.
So we have x² + 6x ___ = 7 ___.
Notice that I created a space on each side of the equation.
The space is what we need to complete the square.
The number that goes in the spaces comes from half the coefficient of the
middle term squared, which in this case is half of 6, or 3, squared, which is 9.
So we add 9 to both sides of the equation.
Once we have completed the square, out trinomial will always factor as a binomial squared, and the number that goes inside the binomial will always be half the coefficient of the middle term of the trinomial.
So we have (x + 3)² = 16.
Now square root both sides to get x + 3 = ± 4
So x + 3 = 4 or x + 3 = -4.
Solving each equation from here, we get x = 1 or x = -7.
So our solution set is {1, -7}.