Solve for all values of xx by factoring.x, squared, minus, 11, x, plus, 22, equals, minus, 2x 2 −11x+22=−2

The equation you've given is x^2 - 11x + 22 = -2.

First, let's simplify this equation by moving -2 to the other side of the equation. This gives us:

x^2 - 11x + 22 + 2 = 0

Which simplifies to:

x^2 - 11x + 24 = 0

Next, we factor the quadratic equation. We're looking for two numbers that multiply to 24 and add to -11. Those numbers are -8 and -3. So, we can write the equation as:

(x - 8)(x - 3) = 0

Setting each factor equal to zero gives the solutions to the equation:

x - 8 = 0 => x = 8

x - 3 = 0 => x = 3

So, the solutions to the equation x^2 - 11x + 24 = 0 are x = 8 and x = 3.