SOLUTION: Solve the following quadratic equations by factoring or by any of the techniques. 4x^2 - 8x + 3 =5 Thanks

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Question 47373: Solve the following quadratic equations by factoring or by any of the techniques.
4x^2 - 8x + 3 =5
Thanks
Answer by beccap528(1) About Me  (Show Source):
You can put this solution on YOUR website!
4x^2 - 8x + 3 =5
First you must subtract 5 from both sides so that you have a quadratic that equals 0. Your new problem is now:
4x^2 - 8x - 2 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-8x%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=%28-8%29%5E2-4%2A4%2A-2=96.

Discriminant d=96 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+96+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+96+%29%29%2F2%5C4+=+2.22474487139159
x%5B2%5D+=+%28-%28-8%29-sqrt%28+96+%29%29%2F2%5C4+=+-0.224744871391589

Quadratic expression 4x%5E2%2B-8x%2B-2 can be factored:
4x%5E2%2B-8x%2B-2+=+4%28x-2.22474487139159%29%2A%28x--0.224744871391589%29
Again, the answer is: 2.22474487139159, -0.224744871391589. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-8%2Ax%2B-2+%29