SOLUTION: x^2+(x+1)^2=100

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Question 614981: x^2+(x+1)^2=100
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+(x+1)^2=100
x^2+(x+1)(x+1)=100
x^2+x^2+2x+1=100
2x^2+2x+1=100
2x^2+2x-99=0
apply the "quadratic formula" to get:
x = {6.55, -7.55}
.
details of quadratic formula follows:
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B2x%2B-99+=+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=%282%29%5E2-4%2A2%2A-99=796.

Discriminant d=796 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+796+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+796+%29%29%2F2%5C2+=+6.55336798983294
x%5B2%5D+=+%28-%282%29-sqrt%28+796+%29%29%2F2%5C2+=+-7.55336798983294

Quadratic expression 2x%5E2%2B2x%2B-99 can be factored:
2x%5E2%2B2x%2B-99+=+2%28x-6.55336798983294%29%2A%28x--7.55336798983294%29
Again, the answer is: 6.55336798983294, -7.55336798983294. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B2%2Ax%2B-99+%29