SOLUTION: Solve by completing the square. x^2 + 2x – 8 = 0

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Question 104074: Solve by completing the square.
x^2 + 2x – 8 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B2x-8=0 Start with the given equation


x%5E2%2B2x=8 Add 8 to both sides


Take half of the x coefficient 2 to get 1 (ie 2%2F2=1)
Now square 1 to get 1 (ie %281%29%5E2=1)



x%5E2%2B2x%2B1=8%2B1 Add this result (1) to both sides. Now the expression x%5E2%2B2x%2B1 is a perfect square trinomial.




%28x%2B1%29%5E2=8%2B1 Factor x%5E2%2B2x%2B1 into %28x%2B1%29%5E2 (note: if you need help with factoring, check out this solver)



%28x%2B1%29%5E2=9 Combine like terms on the right side

x%2B1=0%2B-sqrt%289%29 Take the square root of both sides

x=-1%2B-sqrt%289%29 Subtract 1 from both sides to isolate x.

So the expression breaks down to
x=-1%2Bsqrt%289%29 or x=-1-sqrt%289%29


x=-1%2B3 or x=-1-3 Take the square root of 9 to get 3


x=2 or x=-4 Now combine like terms

So our answer is
x=2 or x=-4


Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B2x-8%29+ graph of y=x%5E2%2B2x-8

Here we can see that the x-intercepts are x=2 and x=-4, so this verifies our answer.