SOLUTION: I need help factoring the expression completely. the problem is 6x^2+27x+27. Please help me.. Thank You for your time.

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Question 412624: I need help factoring the expression completely.
the problem is 6x^2+27x+27.
Please help me..
Thank You for your time.
Answer by jjordan95(63) About Me  (Show Source):
You can put this solution on YOUR website!
Factoring:
3%282x%5E2%2B9x%2B9%29
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Solving for x.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B27x%2B27+=+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=%2827%29%5E2-4%2A6%2A27=81.

Discriminant d=81 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-27%2B-sqrt%28+81+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2827%29%2Bsqrt%28+81+%29%29%2F2%5C6+=+-1.5
x%5B2%5D+=+%28-%2827%29-sqrt%28+81+%29%29%2F2%5C6+=+-3

Quadratic expression 6x%5E2%2B27x%2B27 can be factored:
6x%5E2%2B27x%2B27+=+6%28x--1.5%29%2A%28x--3%29
Again, the answer is: -1.5, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B27%2Ax%2B27+%29