SOLUTION: 2(8x+1)^2=90 Solve using quadratic formula

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Question 536440: 2(8x+1)^2=90
Solve using quadratic formula
Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
2%288x%2B1%29%5E2=90
Divide by 2 both sides
2%288x%2B1%29%5E2%2F2=90%2F2
cross%282%29%288x%2B1%29%5E2%2F2=cross%2890%29%2Fcross%282%29
%288x%2B1%29%5E2=45
64x%5E2%2B16x%2B1=45
64x%5E2%2B16x%2B1-45=0
64x%5E2%2B16x-44=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 64x%5E2%2B16x%2B-44+=+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=%2816%29%5E2-4%2A64%2A-44=11520.

Discriminant d=11520 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-16%2B-sqrt%28+11520+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2816%29%2Bsqrt%28+11520+%29%29%2F2%5C64+=+0.713525491562421
x%5B2%5D+=+%28-%2816%29-sqrt%28+11520+%29%29%2F2%5C64+=+-0.963525491562421

Quadratic expression 64x%5E2%2B16x%2B-44 can be factored:
64x%5E2%2B16x%2B-44+=+64%28x-0.713525491562421%29%2A%28x--0.963525491562421%29
Again, the answer is: 0.713525491562421, -0.963525491562421. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+64%2Ax%5E2%2B16%2Ax%2B-44+%29