1. **State the problem:** Solve the quadratic equation $288t^2 - 392 = 0$ for $t$. 2. **Formula and rules:** To solve for $t$, isolate $t^2$ and then take the square root of both sides. Remember, when taking the square root, consider both positive and negative roots. 3. **Isolate $t^2$:** $$288t^2 - 392 = 0$$ Add 392 to both sides: $$288t^2 = 392$$ 4. **Divide both sides by 288:** $$t^2 = \frac{392}{288}$$ Simplify the fraction by dividing numerator and denominator by their greatest common divisor 8: $$t^2 = \frac{\cancel{392}49}{\cancel{288}36}$$ 5. **Take the square root of both sides:** $$t = \pm \sqrt{\frac{49}{36}}$$ 6. **Simplify the square root:** $$t = \pm \frac{\sqrt{49}}{\sqrt{36}} = \pm \frac{7}{6}$$ **Final answer:** $$t = \pm \frac{7}{6}$$