SOLUTION: what is the answer to this problem: 4x^2 – 2x – 5 = 0

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Question 456391: what is the answer to this problem: 4x^2 – 2x – 5 = 0
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Use the quadratic formula or complete the square to solve.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-2x%2B-5+=+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=%28-2%29%5E2-4%2A4%2A-5=84.

Discriminant d=84 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+84+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+84+%29%29%2F2%5C4+=+1.39564392373896
x%5B2%5D+=+%28-%28-2%29-sqrt%28+84+%29%29%2F2%5C4+=+-0.89564392373896

Quadratic expression 4x%5E2%2B-2x%2B-5 can be factored:
4x%5E2%2B-2x%2B-5+=+4%28x-1.39564392373896%29%2A%28x--0.89564392373896%29
Again, the answer is: 1.39564392373896, -0.89564392373896. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-2%2Ax%2B-5+%29