SOLUTION: when you square five times a number you get three more than the number

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Question 937547: when you square five times a number you get three more than the number
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
(5n)^2 = n+3
25n^2 - n - 3 = 0
...
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 25x%5E2%2B-1x%2B-3+=+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%2A25%2A-3=301.

Discriminant d=301 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+301+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+301+%29%29%2F2%5C25+=+0.366987031457949
x%5B2%5D+=+%28-%28-1%29-sqrt%28+301+%29%29%2F2%5C25+=+-0.326987031457949

Quadratic expression 25x%5E2%2B-1x%2B-3 can be factored:
25x%5E2%2B-1x%2B-3+=+25%28x-0.366987031457949%29%2A%28x--0.326987031457949%29
Again, the answer is: 0.366987031457949, -0.326987031457949. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+25%2Ax%5E2%2B-1%2Ax%2B-3+%29