Solve for x:
-x^2 + 6 x + 9 = 0
Multiply both sides by -1:
x^2 - 6 x - 9 = 0
Add 9 to both sides:
x^2 - 6 x = 9
Add 9 to both sides:
x^2 - 6 x + 9 = 18
Write the left hand side as a square:
(x - 3)^2 = 18
Take the square root of both sides:
x - 3 = 3 sqrt(2) or x - 3 = -3 sqrt(2)
Add 3 to both sides:
x = 3 + 3 sqrt(2) or x - 3 = -3 sqrt(2)
Add 3 to both sides:
Answer: |x = 3 + 3 sqrt(2) or x = 3 - 3 sqrt(2)
