SOLUTION: I don't understand how to solve this equation: -4x^2-24x+36=0 leaving your answer in radicals... I ended up with 24 plus/minus square root of 1152 over 8. but I don't know how to s

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Question 723272: I don't understand how to solve this equation: -4x^2-24x+36=0 leaving your answer in radicals... I ended up with 24 plus/minus square root of 1152 over 8. but I don't know how to simplify it. Can you please help me?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I don't understand how to solve this equation: -4x^2-24x+36=0 leaving your answer in radicals... I ended up with 24 plus/minus square root of 1152 over 8. but I don't know how to simplify it.
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-4x^2-24x+36=0
You can divide by -4
x^2 + 6x - 9 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B-9+=+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%2A-9=72.

Discriminant d=72 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+72+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+72+%29%29%2F2%5C1+=+1.24264068711928
x%5B2%5D+=+%28-%286%29-sqrt%28+72+%29%29%2F2%5C1+=+-7.24264068711928

Quadratic expression 1x%5E2%2B6x%2B-9 can be factored:
1x%5E2%2B6x%2B-9+=+%28x-1.24264068711928%29%2A%28x--7.24264068711928%29
Again, the answer is: 1.24264068711928, -7.24264068711928. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-9+%29

x+=+-3+-+3sqrt%282%29
x+=+-3+%2B+3sqrt%282%29