SOLUTION: x^2+x+square root x^2+x-2=0

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Question 296842: x^2+x+square root x^2+x-2=0
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
according to what u wrote the equation looks like this:
x%5E2%2Bx%2Bsqrt%28x%5E2%29%2Bx-2=0the root and square cancel
x%5E2%2Bx%2Bx%2Bx-2=0add the like terms
x%5E2%2B3x-2=0quadratic formula
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%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=%283%29%5E2-4%2A1%2A-2=17.

Discriminant d=17 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+17+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+17+%29%29%2F2%5C1+=+0.56155281280883
x%5B2%5D+=+%28-%283%29-sqrt%28+17+%29%29%2F2%5C1+=+-3.56155281280883

Quadratic expression 1x%5E2%2B3x%2B-2 can be factored:
1x%5E2%2B3x%2B-2+=+1%28x-0.56155281280883%29%2A%28x--3.56155281280883%29
Again, the answer is: 0.56155281280883, -3.56155281280883. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-2+%29