SOLUTION: {{{ x^2 + 10x - 2 = 0}}}

Algebra ->  Rational-functions -> SOLUTION: {{{ x^2 + 10x - 2 = 0}}}      Log On


   

Question 256696: +x%5E2+%2B+10x+-+2+=+0
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B10x%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=%2810%29%5E2-4%2A1%2A-2=108.

Discriminant d=108 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+108+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+108+%29%29%2F2%5C1+=+0.196152422706632
x%5B2%5D+=+%28-%2810%29-sqrt%28+108+%29%29%2F2%5C1+=+-10.1961524227066

Quadratic expression 1x%5E2%2B10x%2B-2 can be factored:
1x%5E2%2B10x%2B-2+=+1%28x-0.196152422706632%29%2A%28x--10.1961524227066%29
Again, the answer is: 0.196152422706632, -10.1961524227066. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B10%2Ax%2B-2+%29