SOLUTION: Solve the following quadratic equation by completing the square. X^2+ 4x - 4 = 0

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Question 112076: Solve the following quadratic equation by completing the square.
X^2+ 4x - 4 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B4x-4=0 Start with the given equation


x%5E2%2B4x=4 Add 4 to both sides


Take half of the x coefficient 4 to get 2 (ie 4%2F2=2)
Now square 2 to get 4 (ie %282%29%5E2=4)



x%5E2%2B4x%2B4=4%2B4 Add this result (4) to both sides. Now the expression x%5E2%2B4x%2B4 is a perfect square trinomial.




%28x%2B2%29%5E2=4%2B4 Factor x%5E2%2B4x%2B4 into %28x%2B2%29%5E2 (note: if you need help with factoring, check out this solver)



%28x%2B2%29%5E2=8 Combine like terms on the right side

x%2B2=0%2B-sqrt%288%29 Take the square root of both sides

x=-2%2B-sqrt%288%29 Subtract 2 from both sides to isolate x.

So the expression breaks down to
x=-2%2Bsqrt%288%29 or x=-2-sqrt%288%29


So our answer is approximately
x=0.82842712474619 or x=-4.82842712474619

Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B4x-4%29+ graph of y=x%5E2%2B4x-4


When we use the root finder feature on a calculator, we would find that the x-intercepts are x=0.82842712474619 and x=-4.82842712474619, so this verifies our answer.