SOLUTION: Solve by completing the square x^2 + 8x = 5

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Question 247234: Solve by completing the square
x^2 + 8x = 5
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
take (8/2)^2
4^2=16
add 16 to both sides
x^2 + 8x +16= 21
(x-4)^2=21
get sqrt
x=+\-sqrt(21)
other methods of solving
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B8x%2B-5+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%288%29%5E2-4%2A1%2A-5=84.

Discriminant d=84 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+84+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+84+%29%29%2F2%5C1+=+0.58257569495584
x%5B2%5D+=+%28-%288%29-sqrt%28+84+%29%29%2F2%5C1+=+-8.58257569495584

Quadratic expression 1x%5E2%2B8x%2B-5 can be factored:
1x%5E2%2B8x%2B-5+=+1%28x-0.58257569495584%29%2A%28x--8.58257569495584%29
Again, the answer is: 0.58257569495584, -8.58257569495584. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B-5+%29