SOLUTION: 4^2X+1=X^2 solve

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Question 944900: 4^2X+1=X^2 solve
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
4^2X+1=X^2 solve
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16x+1 = x^2
x^2 - 16x - 1 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-16x%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=%28-16%29%5E2-4%2A1%2A-1=260.

Discriminant d=260 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--16%2B-sqrt%28+260+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+260+%29%29%2F2%5C1+=+16.0622577482985
x%5B2%5D+=+%28-%28-16%29-sqrt%28+260+%29%29%2F2%5C1+=+-0.0622577482985491

Quadratic expression 1x%5E2%2B-16x%2B-1 can be factored:
1x%5E2%2B-16x%2B-1+=+%28x-16.0622577482985%29%2A%28x--0.0622577482985491%29
Again, the answer is: 16.0622577482985, -0.0622577482985491. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-16%2Ax%2B-1+%29

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