SOLUTION: solve each equation for x 2(x-5)^2=3

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Question 99590: solve each equation for x
2(x-5)^2=3
Answer by timmy1729(23) About Me  (Show Source):
You can put this solution on YOUR website!
2%28x-5%29%5E2=3
I would personally expand the %28x-5%29%5E2 first.
That gives us:
2%28x%5E2+-+10x+%2B+25%29+=+3
Then multiply by the 2:
2x%5E2+-+20x+%2B+50+=+3
Then subtract the 3:
2x%5E2+-+20x+%2B+47+=+0
You aren't going to like this, but you have to use the quadratic formula for this one.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-20x%2B47+=+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=%28-20%29%5E2-4%2A2%2A47=24.

Discriminant d=24 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--20%2B-sqrt%28+24+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-20%29%2Bsqrt%28+24+%29%29%2F2%5C2+=+6.22474487139159
x%5B2%5D+=+%28-%28-20%29-sqrt%28+24+%29%29%2F2%5C2+=+3.77525512860841

Quadratic expression 2x%5E2%2B-20x%2B47 can be factored:
2x%5E2%2B-20x%2B47+=+2%28x-6.22474487139159%29%2A%28x-3.77525512860841%29
Again, the answer is: 6.22474487139159, 3.77525512860841. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-20%2Ax%2B47+%29