1. **State the problem:** Solve the quadratic equation $$84 = 7u^2 + 28$$ for the real number $u$, rounding to the nearest hundredth. 2. **Rewrite the equation:** Subtract 84 from both sides to set the equation to zero: $$7u^2 + 28 - 84 = 0$$ 3. **Simplify:** $$7u^2 - 56 = 0$$ 4. **Divide both sides by 7 to simplify:** $$\cancel{7}u^2 - \cancel{7}8 = 0$$ which simplifies to $$u^2 - 8 = 0$$ 5. **Isolate $u^2$:** $$u^2 = 8$$ 6. **Take the square root of both sides:** $$u = \pm \sqrt{8}$$ 7. **Simplify the square root:** $$u = \pm \sqrt{4 \times 2} = \pm 2\sqrt{2}$$ 8. **Calculate the decimal values:** $$u = \pm 2 \times 1.4142 = \pm 2.83$$ **Final answer:** $$u = 2.83, -2.83$$