Question 191655
Although your answer is correct, you solved it by factoring instead of "completing the square".
.
9x^2+18x=-8 
.
9(x^2+2x) = -8 
9(x^2+2x+__) = -8 
Take half the 'b' term and square it.  Then balance the right with what you just added to the left side.
9(x^2+2x+1) = -8 + 9
9(x+1)^2 = 1
Dividing both sides by 9:
(x+1)^2 = 1/9
Taking the square root of both sides:
(x+1) = +-(1/3) (that's plus or minus 1/3)
x = +-(1/3) - 1
.
x = 1/3 - 1 = 1/3 - 3/3 = -2/3
x = -1/3 - 1 = -1/3 - 3/3 = -4/3
.
x = {-4/3, -2/3}