SOLUTION: Solve by completing the square x^2+18x+80=0 Thank you

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Question 98234: Solve by completing the square
x^2+18x+80=0
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B18x%2B80=0 Start with the given equation


x%5E2%2B18x=-80 Subtract 80 from both sides


Take half of the x coefficient 18 to get 9 (ie 18%2F2=9)
Now square 9 to get 81 (ie %289%29%5E2=81)



x%5E2%2B18x%2B81=-80%2B81 Add this result (81) to both sides. Now the expression x%5E2%2B18x%2B81 is a perfect square trinomial.




%28x%2B9%29%5E2=-80%2B81 Factor x%5E2%2B18x%2B81 into %28x%2B9%29%5E2 (note: if you need help with factoring, check out this solver)



%28x%2B9%29%5E2=1 Combine like terms on the right side

x%2B9=0%2B-sqrt%281%29 Take the square root of both sides

x=-9%2B-sqrt%281%29 Subtract 9 from both sides to isolate x.

So the expression breaks down to
x=-9%2Bsqrt%281%29 or x=-9-sqrt%281%29


x=-9%2B1 or x=-9-1 Take the square root of 1 to get 1


x=-8 or x=-10 Now combine like terms

So our answer is
x=-8 or x=-10


Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B18x%2B80%29+ graph of y=x%5E2%2B18x%2B80

Here we can see that the x-intercepts are x=-8 and x=-10, so this verifies our answer.