x2=-x+2

To solve the equation \( x^2 = -x + 2 \), you can first rearrange it into standard quadratic form. Start by adding \( x \) and subtracting 2 from both sides:

\[ x^2 + x - 2 = 0 \]

Now, you can factor the quadratic equation. We need two numbers that multiply to \(-2\) (the constant term) and add up to \(1\) (the coefficient of \(x\)). Those numbers are \(2\) and \(-1\).

So, we can factor the equation as:

\[ (x + 2)(x - 1) = 0 \]

Now we can set each factor to zero:

1. \( x + 2 = 0 \)

   • \( x = -2 \)

2. \( x - 1 = 0 \)

   • \( x = 1 \)

Thus, the solutions to the equation \( x^2 = -x + 2 \) are:

\[ x = -2 \quad \text{and} \quad x = 1 \]