Solve by Completing the Square x^2-2x-2=0

Problem

x2−2*x−2=0

Solution

1. Isolate the constant term by adding 2 to both sides of the equation.

x2−2*x=2

2. Identify the coefficient of the x term, which is −2 and calculate the value needed to complete the square by taking half of it and squaring the result: ((−2)/2)2=1

(−1)2=1

3. Add this value to both sides of the equation to maintain equality.

x2−2*x+1=2+1

4. Factor the left side as a perfect square trinomial and simplify the right side.

(x−1)2=3

5. Take the square root of both sides, remembering to include both the positive and negative roots.

x−1=±√(,3)

6. Solve for x by adding 1 to both sides.

x=1±√(,3)

Final Answer

x=1±√(,3)

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