SOLUTION: Solve the equation by completing the square x^2 + 4x - 21 = 0

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Question 100954: Solve the equation by completing the square
x^2 + 4x - 21 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B4x-21=0 Start with the given equation


x%5E2%2B4x=21 Add 21 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=21%2B4 Add this result (4) to both sides. Now the expression x%5E2%2B4x%2B4 is a perfect square trinomial.




%28x%2B2%29%5E2=21%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=25 Combine like terms on the right side

x%2B2=0%2B-sqrt%2825%29 Take the square root of both sides

x=-2%2B-sqrt%2825%29 Subtract 2 from both sides to isolate x.

So the expression breaks down to
x=-2%2Bsqrt%2825%29 or x=-2-sqrt%2825%29


x=-2%2B5 or x=-2-5 Take the square root of 25 to get 5


x=3 or x=-7 Now combine like terms

So our answer is
x=3 or x=-7


Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B4x-21%29+ graph of y=x%5E2%2B4x-21

Here we can see that the x-intercepts are x=3 and x=-7, so this verifies our answer.