SOLUTION: Solve using quadratic formula: 1.) 3a^2=6a-3 2.) x^2=-3x+40 3.) 9x^2-11=6x 4.) 4a^2-8+a Thank you

Algebra ->  Rational-functions -> SOLUTION: Solve using quadratic formula: 1.) 3a^2=6a-3 2.) x^2=-3x+40 3.) 9x^2-11=6x 4.) 4a^2-8+a Thank you      Log On


   

Question 594939: Solve using quadratic formula:
1.) 3a^2=6a-3
2.) x^2=-3x+40
3.) 9x^2-11=6x
4.) 4a^2-8+a
Thank you
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve using quadratic formula:
1.) 3a^2=6a-3
2.) x^2=-3x+40
x%5E2+%2B+3x+-+40+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-40+=+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=%283%29%5E2-4%2A1%2A-40=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+169+%29%29%2F2%5C1+=+5
x%5B2%5D+=+%28-%283%29-sqrt%28+169+%29%29%2F2%5C1+=+-8

Quadratic expression 1x%5E2%2B3x%2B-40 can be factored:
1x%5E2%2B3x%2B-40+=+%28x-5%29%2A%28x--8%29
Again, the answer is: 5, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-40+%29

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Do the others the same way.
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3.) 9x^2-11=6x
4.) 4a^2-8+a
Thank you