SOLUTION: x2-2x-2=0

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Question 281453: x2-2x-2=0
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x2-2x-2=0
x^2-2x=2
complete the square
1/2*2=1
1^2=1
add one to both sides
x^2-2x+1=3
(x-1)^2=3
x-1=+sqrt(3)
x=1+sqrt(3)

x-1=-sqrt(3)
x=1-sqrt(3)
answer
x=1+sqrt(3), 1-sqrt(3)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-2+=+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=%28-2%29%5E2-4%2A1%2A-2=12.

Discriminant d=12 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+12+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+12+%29%29%2F2%5C1+=+2.73205080756888
x%5B2%5D+=+%28-%28-2%29-sqrt%28+12+%29%29%2F2%5C1+=+-0.732050807568877

Quadratic expression 1x%5E2%2B-2x%2B-2 can be factored:
1x%5E2%2B-2x%2B-2+=+1%28x-2.73205080756888%29%2A%28x--0.732050807568877%29
Again, the answer is: 2.73205080756888, -0.732050807568877. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-2+%29