1. **State the problem:** Solve the quadratic equation $2x^2 - 8x + 8 = 4x - 8$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$2x^2 - 8x + 8 - 4x + 8 = 0$$ Simplify: $$2x^2 - 12x + 16 = 0$$ 3. **Divide the entire equation by 2** to simplify: $$x^2 - 6x + 8 = 0$$ 4. **Use the quadratic formula:** For $ax^2 + bx + c = 0$, solutions are $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ Here, $a=1$, $b=-6$, $c=8$. 5. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-6)^2 - 4(1)(8) = 36 - 32 = 4$$ 6. **Find the roots:** $$x = \frac{-(-6) \pm \sqrt{4}}{2(1)} = \frac{6 \pm 2}{2}$$ 7. **Calculate each root:** - $$x_1 = \frac{6 + 2}{2} = \frac{8}{2} = 4$$ - $$x_2 = \frac{6 - 2}{2} = \frac{4}{2} = 2$$ **Final answer:** The solutions to the equation are $x=4$ and $x=2$.