SOLUTION: solve by completing the square: x^2-2x-1=0

Question 116770: solve by completing the square: x^2-2x-1=0
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation

Add 1 to both sides

Take half of the x coefficient -2 to get -1 (ie )
Now square -1 to get 1 (ie )

Add this result (1) to both sides. Now the expression is a perfect square trinomial.

Factor into (note: if you need help with factoring, check out this solver)

Combine like terms on the right side

Take the square root of both sides

Add 1 to both sides to isolate x.

So the expression breaks down to
or

So our answer is approximately
or

Here is visual proof

graph of

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

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