SOLUTION: How do I solve this eqaution by completing the sqaure? 5x^2-10x+2=0

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Question 194265: How do I solve this eqaution by completing the sqaure?
5x^2-10x+2=0
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
5x^2-10x+2=0
Isolate the x-terms on the left:
5x^2-10x = -2
Divide both sides by 5:
x^2-2x = -2/5
Now, we can complete the square on the left:
(x^2-2x+___) = -2/5
(x^2-2x+1) = -2/5+1
(x-1)^2 = -2/5 + 5/5
(x-1)^2 = 3/5
Take the square root of both sides:
x-1 = sqrt(3/5) = sqrt(15)/5
x = sqrt(15)/5 + 1
x = 1 +- sqrt(15)/5
or
x = (5 +- sqrt(15))/5
.
To check, we can solve it using the quadratic equation which yields:
x = {1.7746, 0.2254}
Which gives you the same answers.
Details of quadratic to follow:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-10x%2B2+=+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=%28-10%29%5E2-4%2A5%2A2=60.

Discriminant d=60 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+60+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+60+%29%29%2F2%5C5+=+1.77459666924148
x%5B2%5D+=+%28-%28-10%29-sqrt%28+60+%29%29%2F2%5C5+=+0.225403330758517

Quadratic expression 5x%5E2%2B-10x%2B2 can be factored:
5x%5E2%2B-10x%2B2+=+5%28x-1.77459666924148%29%2A%28x-0.225403330758517%29
Again, the answer is: 1.77459666924148, 0.225403330758517. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-10%2Ax%2B2+%29