SOLUTION: Solve 5x^2 + 1= 5x

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Question 82875: Solve 5x^2 + 1= 5x
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
5x%5E2+%2B+1=+5x Start with the given equation

5x%5E2+%2B+1+-5x=+0 Subtract 5x from both sides

5x%5E2+-5x%2B+1+=+0 Rearrange the terms in ax%5E2%2Bbx%2Bc form

Now we can use the quadratic formula to solve for x:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-5x%2B1+=+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=%28-5%29%5E2-4%2A5%2A1=5.

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

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+5+%29%29%2F2%5C5+=+0.723606797749979
x%5B2%5D+=+%28-%28-5%29-sqrt%28+5+%29%29%2F2%5C5+=+0.276393202250021

Quadratic expression 5x%5E2%2B-5x%2B1 can be factored:
5x%5E2%2B-5x%2B1+=+5%28x-0.723606797749979%29%2A%28x-0.276393202250021%29
Again, the answer is: 0.723606797749979, 0.276393202250021. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-5%2Ax%2B1+%29