SOLUTION: 2x^2 - 6x + 2 = 0

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Question 618018: 2x^2 - 6x + 2 = 0
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
2x^2 - 6x + 2 = 0
divide both sides by 2:
x^2 - 3x + 1 = 0
Since you can't factor, apply the "quadratic formula" to get:
x = {2.618, 0.382}
.
Details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-3x%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=%28-3%29%5E2-4%2A1%2A1=5.

Discriminant d=5 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+5+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+5+%29%29%2F2%5C1+=+2.61803398874989
x%5B2%5D+=+%28-%28-3%29-sqrt%28+5+%29%29%2F2%5C1+=+0.381966011250105

Quadratic expression 1x%5E2%2B-3x%2B1 can be factored:
1x%5E2%2B-3x%2B1+=+1%28x-2.61803398874989%29%2A%28x-0.381966011250105%29
Again, the answer is: 2.61803398874989, 0.381966011250105. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B1+%29