Answer
The solutions are $3$ and $-9$, and the solution set is {$3, -9$}.
Work Step by Step
$x^2 - 6x + 9 = 36$
Subtract $9$ from both sides to isolate the binomial $x^2 - 6x$.
$x^2 - 6x + 9 -9 = 36-9$
$x^2 - 6x = 27$
The coefficient of the x-term is $-6$.
Half of $-6$ is $-3$, and $-3^2 = 9$.
Thus, add $9$ to both sides of the equation to complete the square.
$x^2 - 6x + 9= 27 +9$
$x^2 + 6x +9 = 36$
$(x-3)^2 = 36$
$ x -3 =\sqrt36$ or $ x -3 =-\sqrt36$
$x = -3+6$ or $x = -3-6$
The solutions are $3$ and $-9$, and the solution set is {$3, -9$}.
