Solve by first completing the square.x2+2x−2=0𝑥2+2𝑥−2=0x=𝑥=  +√+ or x=𝑥=  −√−

Sure, let's solve the quadratic equation step by step by completing the square:

1. The given equation is x^2 + 2x - 2 = 0.

2. To complete the square, we need to make the left side of the equation a perfect square. We can do this by adding and subtracting (b/2a)^2 to the equation. Here, a = 1 (the coefficient of x^2) and b = 2 (the coefficient of x). So, (b/2a)^2 = (2/2*1)^2 = 1^2 = 1.

3. Adding and subtracting 1 to the equation, we get x^2 + 2x + 1 - 1 - 2 = 0.

4. The first three terms on the left side of the equation now form a perfect square: (x + 1)^2. So, the equation becomes (x + 1)^2 - 1 - 2 = 0.

5. Simplifying the equation, we get (x + 1)^2 - 3 = 0.

6. Now, we can solve for x by first adding 3 to both sides of the equation to isolate the square on one side: (x + 1)^2 = 3.

7. Then, we take the square root of both sides of the equation. Remember that the square root of a number y is both positive and negative. So, we get x + 1 = sqrt(3) and x + 1 = -sqrt(3).

8. Finally, we subtract 1 from both sides of both equations to solve for x. So, the solutions to the equation are x = sqrt(3) - 1 and x = -sqrt(3) - 1.