1. **State the problem:** Solve the equation $$8x^4 - 3 = 2$$ for $x$. 2. **Rewrite the equation:** Add 3 to both sides to isolate the term with $x$: $$8x^4 = 2 + 3$$ $$8x^4 = 5$$ 3. **Divide both sides by 8:** $$x^4 = \frac{5}{8}$$ 4. **Take the fourth root of both sides:** $$x = \pm \sqrt[4]{\frac{5}{8}}$$ 5. **Calculate the numerical value:** First, calculate the fraction: $$\frac{5}{8} = 0.625$$ Then take the fourth root: $$x = \pm 0.625^{\frac{1}{4}}$$ Using a calculator: $$x \approx \pm 0.8881$$ **Final answer:** $$x \approx \pm 0.8881$$ (correct to 4 significant figures)