SOLUTION: What is the value of x is this equation 2x(2x-1) = 4

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Question 754217: What is the value of x is this equation 2x(2x-1) = 4
Found 2 solutions by Alan3354, rothauserc:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What is the value of x is this equation 2x(2x-1) = 4
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2x(2x-1) = 4
x(2x-1) = 2
2x%5E2+-+x+-+2+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-1x%2B-2+=+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=%28-1%29%5E2-4%2A2%2A-2=17.

Discriminant d=17 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+17+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+17+%29%29%2F2%5C2+=+1.28077640640442
x%5B2%5D+=+%28-%28-1%29-sqrt%28+17+%29%29%2F2%5C2+=+-0.780776406404415

Quadratic expression 2x%5E2%2B-1x%2B-2 can be factored:
2x%5E2%2B-1x%2B-2+=+%28x-1.28077640640442%29%2A%28x--0.780776406404415%29
Again, the answer is: 1.28077640640442, -0.780776406404415. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-1%2Ax%2B-2+%29

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
What is the value of x is this equation 2x(2x-1) = 4
2x(2x-1) = 4
4x^2 -2x = 4
divide both sides of = by 2
2x^2 -x = 2
2x^2 -x -2 = 0
now use quadratic formula
1 plus or minus sqrt(1 - 4*(2)*(-2)) / 2*2
1 plus or minus sqrt(1+16) / 4
1 plus or minus sqrt(17) / 4
x = (1 + sqrt(17)) / 4 = 1.28
x = (1 - sqrt(17)) / 4 = -.78