X2=-2x+1

To solve the equation \( x^2 = -2x + 1 \), we can first rearrange it into standard form. Here's how you can do it:

1. Move all terms to one side of the equation: \[ x^2 + 2x - 1 = 0 \]

2. Now you can use the quadratic formula to solve for \( x \): \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \( a = 1 \), \( b = 2 \), and \( c = -1 \).

3. Calculate the discriminant (\( b^2 - 4ac \)): \[ b^2 - 4ac = 2^2 - 4(1)(-1) = 4 + 4 = 8 \]

4. Now plug the values into the quadratic formula: \[ x = \frac{-2 \pm \sqrt{8}}{2(1)} = \frac{-2 \pm 2\sqrt{2}}{2} \] Simplifying further gives: \[ x = -1 \pm \sqrt{2} \]

5. So, the solutions are: \[ x = -1 + \sqrt{2} \quad \text{and} \quad x = -1 - \sqrt{2} \]

These are the two solutions to the equation \( x^2 = -2x + 1 \).