You can put this solution on YOUR website! x^2-4x-1=0
Rewrite as:
x^2 - 4x = 1
We need to add a constant to both sides so that the left side becomes a perfect suqare of the form (x+a)^2.
Since the middle term is -4x we know that the constant needs to be -4/2 = -2 which when squared is (-2)^2 = 4. So we add 4 to both sides of the equation above:
x^2 - 4x + 4 = 1 + 4
(x-2)^ = 5
Taking the square root of both sides above we have x-2 = sqrt(5) or x-2 = -sqrt(5) so
x = 2+sqrt(5) or x = 2-sqrt(5)
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