Question 191655: Solve by completing the square. First divide to make sure that the coefficient of x^2 is 1
9x^2+18x=-8
I completed the square but dividing to make sure that the coefficient is 1 I am not understanding. Here is what I did...
9x^2+18x+8=0
(3x+4)(3x+2)
3x+4=0 3x+2=0
3x=-4 3x=-2
x=-4/3 x=-2/3
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Although your answer is correct, you solved it by factoring instead of "completing the square".
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9x^2+18x=-8
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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
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x = 1/3 - 1 = 1/3 - 3/3 = -2/3
x = -1/3 - 1 = -1/3 - 3/3 = -4/3
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x = {-4/3, -2/3}
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