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

Question 194265: How do I solve this eqaution by completing the sqaure?
5x^2-10x+2=0
Answer by nerdybill(7384) (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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=60 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.77459666924148, 0.225403330758517. Here's your graph:

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