SOLUTION: Solve: x^2 - 4x - 1=0 by completing the square.

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Question 109388: Solve: x^2 - 4x - 1=0 by completing the square.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-4x-1=0 Start with the given equation


x%5E2-4x=1 Add 1 to both sides


Take half of the x coefficient -4 to get -2 (ie -4%2F2=-2)
Now square -2 to get 4 (ie %28-2%29%5E2=4)



x%5E2-4x%2B4=1%2B4 Add this result (4) to both sides. Now the expression x%5E2-4x%2B4 is a perfect square trinomial.




%28x-2%29%5E2=1%2B4 Factor x%5E2-4x%2B4 into %28x-2%29%5E2 (note: if you need help with factoring, check out this solver)



%28x-2%29%5E2=5 Combine like terms on the right side

x-2=0%2B-sqrt%285%29 Take the square root of both sides

x=2%2B-sqrt%285%29 Add 2 to both sides to isolate x.

So the expression breaks down to
x=2%2Bsqrt%285%29 or x=2-sqrt%285%29


So our answer is approximately
x=4.23606797749979 or x=-0.23606797749979

Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-4x-1%29+ graph of y=x%5E2-4x-1


When we use the root finder feature on a calculator, we would find that the x-intercepts are x=4.23606797749979 and x=-0.23606797749979, so this verifies our answer.