1. **State the problem:** Solve the equation $$0 = 24x + 2x^2 - 95$$ for $x$ and round the solutions to the nearest integer. 2. **Rewrite the equation:** The equation is a quadratic equation in standard form: $$2x^2 + 24x - 95 = 0$$ 3. **Use the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solutions are given by: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ Here, $a=2$, $b=24$, and $c=-95$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 24^2 - 4 \times 2 \times (-95) = 576 + 760 = 1336$$ 5. **Find the square root of the discriminant:** $$\sqrt{1336} \approx 36.55$$ 6. **Calculate the two solutions:** $$x_1 = \frac{-24 + 36.55}{2 \times 2} = \frac{12.55}{4} = 3.1375$$ $$x_2 = \frac{-24 - 36.55}{4} = \frac{-60.55}{4} = -15.1375$$ 7. **Round to the nearest integer:** $$x_1 \approx 3$$ $$x_2 \approx -15$$ **Final answer:** The solutions rounded to the nearest integer are $x = 3$ and $x = -15$.