2x-x в квадрате=-8

Let's solve the equation: \[ 2x - x^2 = -8 \] Step 1: Rewrite the equation in standard quadratic form: \[ -x^2 + 2x + 8 = 0 \] Multiply both sides by -1 to make the coefficient of \(x^2\) positive: \[ x^2 - 2x - 8 = 0 \] Step 2: Solve the quadratic equation using the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \(a=1\), \(b=-2\), and \(c=-8\). Step 3: Calculate the discriminant: \[ D = b^2 - 4ac = (-2)^2 - 4 \times 1 \times (-8) = 4 + 32 = 36 \] Step 4: Find the roots: \[ x = \frac{-(-2) \pm \sqrt{36}}{2 \times 1} = \frac{2 \pm 6}{2} \] So, \[ x = \frac{2 + 6}{2} = \frac{8}{2} = 4 \] and \[ x = \frac{2 - 6}{2} = \frac{-4}{2} = -2 \] **Final answer:** \[ x = 4 \quad \text{or} \quad x = -2 \]