SOLUTION: 4x^2 - 4x - 1 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 4x^2 - 4x - 1 = 0       Log On


   

Question 735667: 4x^2 - 4x - 1 = 0

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-4x%2B-1+=+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=%28-4%29%5E2-4%2A4%2A-1=32.

Discriminant d=32 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+32+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+32+%29%29%2F2%5C4+=+1.20710678118655
x%5B2%5D+=+%28-%28-4%29-sqrt%28+32+%29%29%2F2%5C4+=+-0.207106781186548

Quadratic expression 4x%5E2%2B-4x%2B-1 can be factored:
4x%5E2%2B-4x%2B-1+=+%28x-1.20710678118655%29%2A%28x--0.207106781186548%29
Again, the answer is: 1.20710678118655, -0.207106781186548. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-4%2Ax%2B-1+%29