SOLUTION: Solve by completing the square {{{x^2+8 x=-15}}}

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Question 143032: Solve by completing the square

x%5E2%2B8+x=-15
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B8+x=-15 Start with the given equation


Take half of the x coefficient 8 to get 4 (ie %281%2F2%29%288%29=4).

Now square 4 to get 16 (ie %284%29%5E2=%284%29%284%29=16)


x%5E2%2B8+x%2B16=-15%2B16 Add this value to both sides


x%5E2%2B8+x%2B16=1 Combine like terms


%28x%2B4%29%5E2=1 Now factor x%5E2%2B8x%2B16 to get %28x%2B4%29%5E2


x%2B4=0%2B-sqrt%281%29 Take the square root of both sides


x%2B4=1 or x%2B4=-1 Simplify


x=-3 or x=-5 Simplify Subtract 4 from both sides in each case



So the solutions are x=-3 or x=-5



Notice if we graph we can see that the roots are x=-3 and x=-5. So this verifies our answer.

graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C+x%5E2%2B8x%2B15%29