SOLUTION: x^2+6x+6=0 solve with quadratic formula

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Question 240518: x^2+6x+6=0 solve with quadratic formula
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+6x+6=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B6+=+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=%286%29%5E2-4%2A1%2A6=12.

Discriminant d=12 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+12+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+12+%29%29%2F2%5C1+=+-1.26794919243112
x%5B2%5D+=+%28-%286%29-sqrt%28+12+%29%29%2F2%5C1+=+-4.73205080756888

Quadratic expression 1x%5E2%2B6x%2B6 can be factored:
1x%5E2%2B6x%2B6+=+%28x--1.26794919243112%29%2A%28x--4.73205080756888%29
Again, the answer is: -1.26794919243112, -4.73205080756888. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B6+%29

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= -3 ± sqrt(3)