SOLUTION: solve using the quadratic formula, simplify the exact answer: 2x^2+12x=-2x^2-6

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: solve using the quadratic formula, simplify the exact answer: 2x^2+12x=-2x^2-6      Log On


   

Question 183997: solve using the quadratic formula, simplify the exact answer:
2x^2+12x=-2x^2-6
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
solve using the quadratic formula, simplify the exact answer:
2x^2+12x=-2x^2-6
4x%5E2+%2B+12x+%2B+6+=+0
2x%5E2+%2B+6x+%2B+3+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B6x%2B3+=+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%2A2%2A3=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%5C2+=+-0.633974596215561
x%5B2%5D+=+%28-%286%29-sqrt%28+12+%29%29%2F2%5C2+=+-2.36602540378444

Quadratic expression 2x%5E2%2B6x%2B3 can be factored:
2x%5E2%2B6x%2B3+=+%28x--0.633974596215561%29%2A%28x--2.36602540378444%29
Again, the answer is: -0.633974596215561, -2.36602540378444. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B6%2Ax%2B3+%29

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So it's
-(3/2) + sqrt(3)/2
-(3/2) - sqrt(3)/2