1. **State the problem:** Solve the equation $9.4 + 64x^2 = 53$ for $x$. 2. **Rewrite the equation:** $$9.4 + 64x^2 = 53$$ 3. **Isolate the term with $x^2$:** Subtract $9.4$ from both sides: $$64x^2 = 53 - 9.4$$ $$64x^2 = 43.6$$ 4. **Solve for $x^2$:** Divide both sides by $64$: $$x^2 = \frac{43.6}{64}$$ Show the cancellation: $$x^2 = \frac{\cancel{43.6}}{\cancel{64}}$$ (Here, no common factors to cancel, so fraction remains as is.) 5. **Simplify the fraction:** $$x^2 = 0.68125$$ 6. **Take the square root of both sides:** $$x = \pm \sqrt{0.68125}$$ 7. **Calculate the square root:** $$x \approx \pm 0.8255$$ **Final answer:** $$x \approx \pm 0.8255$$