Question 194265
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:
*[invoke quadratic "x", 5, -10, 2 ]