SOLUTION: Solve for the unknow.Which would be X. 0=2x(x²+1)ˉ½-1

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Question 190265: Solve for the unknow.Which would be X.
0=2x(x²+1)ˉ½-1
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
.
0+=+2x%28x%5E2%2B1%29%5E%28-1%2F2%29+-+1
0+=+2x%2F%28x%5E2%2B1%29%5E%281%2F2%29+-+1
Now, multiply both sides by %28x%5E2%2B1%29%5E%281%2F2%29
0+=+2x+-+%28x%5E2%2B1%29%5E%281%2F2%29
%28x%5E2%2B1%29%5E%281%2F2%29+=+2x
Squaring both sides:
x%5E2%2B1+=+4x%5E2
Moving all terms to the right:
0+=+4x%5E2+-+x%5E2+-+1
Solving with the quadratic equation yields:
x = {0.6404, -0.3904}
.
Details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-1x%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=%28-1%29%5E2-4%2A4%2A-1=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%5C4+=+0.640388203202208
x%5B2%5D+=+%28-%28-1%29-sqrt%28+17+%29%29%2F2%5C4+=+-0.390388203202208

Quadratic expression 4x%5E2%2B-1x%2B-1 can be factored:
4x%5E2%2B-1x%2B-1+=+4%28x-0.640388203202208%29%2A%28x--0.390388203202208%29
Again, the answer is: 0.640388203202208, -0.390388203202208. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-1%2Ax%2B-1+%29