SOLUTION: 1.) 9x^2+18x=-8 (solve by completing the square an coefficient of x^2 is 1) I'm looking for the processes of these. The book examples don't help.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 1.) 9x^2+18x=-8 (solve by completing the square an coefficient of x^2 is 1) I'm looking for the processes of these. The book examples don't help.       Log On


   

Question 1026809: 1.) 9x^2+18x=-8 (solve by completing the square an coefficient of x^2 is 1)
I'm looking for the processes of these. The book examples don't help.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by MathTherapy(10552) About Me  (Show Source):
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1.) 9x^2+18x=-8 (solve by completing the square an coefficient of x^2 is 1)
I'm looking for the processes of these. The book examples don't help. 


In response to: "Comment from student: Thank you. It was 18 and not 19, sorry."


9x%5E2+%2B+18x+=+-+8

9%28x%5E2+%2B+2x%29+=+9%28-+8%2F9%29 ------ Factoring out 9 to get a coefficient of 1 on x%5E2

x%5E2+%2B+2x+=+-+8%2F9

x%5E2+%2B+2x+%2B+%28%281%2F2%29b%29%5E2+=+-+8%2F9+%2B+%28%281%2F2%29+%2A+b%29%5E2 ---- Halving the value of b, squaring the result, then adding to both sides

x%5E2+%2B+2x+%2B+%28%281%2F2%29+%2A+2%29%5E2+=+-+8%2F9+%2B+%28%281%2F2%29+%2A+2%29%5E2 ---- Substituting + 2 for b

x%5E2+%2B+2x+%2B+1%5E2+=+-+8%2F9+%2B+1%5E2 

%28x+%2B+1%29%5E2+=+-+8%2F9+%2B+1

%28x+%2B+1%29%5E2+=+-+8%2F9+%2B+9%2F9

%28x+%2B+1%29%5E2+=+1%2F9

sqrt%28%28x+%2B+1%29%5E2%29+=+%22+%22%2B-+sqrt%281%2F9%29 ------- Taking square root of both sides

x+%2B+1+=+%22+%22%2B-+1%2F3

x+=+%22+%22%2B-+1%2F3+-+1