SOLUTION: solve for x: x^2-6x+4=0

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Question 603119: solve for x:
x^2-6x+4=0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You can solve x%5E2-6x%2B4=0 by "completing the square" or you can apply the quadratic formula.

COMPLETING THE SQUARE:
x%5E2-6x%2B4=0 --> x%5E2-6x=-4
At this point you would recognize that the left hand side of the equation resembles the square
%28x-3%29%5E2=x%5E2-6x%2B9
So, you add 9 to both sides of x%5E2-6x=-4 to get the equivalent equation with the complete square on the left hand side:
x%5E2-6x%2B9=-4%2B9 --> x%5E2-6x%2B9=5 ---> %28x-3%29%5E2=5
At this point, you know that either
x-3=sqrt%285%29 or x-3=-sqrt%285%29
Adding 3 to both sides of the two equations above, you get the two solutions
x=3%2Bsqrt%285%29 and x=3-sqrt%285%29,
which can be summarized as
x=3+%2B-+sqrt%285%29

THE QUADRATIC FORMULA
All quadratic equations are of the form
ax%5E2%2Bbx%2Bc=0 where a, b, and c are the coefficients which could be any number, with the only restriction that a cannot be zero.
The solution is given by the quadratic formula:
x=%28-b+%2B-+sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29
In the equation x%5E2-6x%2B4=0,
a=1, b=-6 and c=4, so the quadratic formula gives us

That can be simplified like this