Solve For X C0E2B5

1. **State the problem:** Solve the equation $$A = 4x^2 + 8xh$$ for the variable $$x$$. 2. **Write the equation:** $$A = 4x^2 + 8xh$$. 3. **Rearrange the equation:** Move all terms to one side to form a quadratic in $$x$$: $$4x^2 + 8xh - A = 0$$ 4. **Identify coefficients:** This is a quadratic equation in $$x$$ with: $$a = 4, \quad b = 8h, \quad c = -A$$ 5. **Use the quadratic formula:** $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ Substitute the values: $$x = \frac{-8h \pm \sqrt{(8h)^2 - 4 \cdot 4 \cdot (-A)}}{2 \cdot 4}$$ 6. **Simplify under the square root:** $$x = \frac{-8h \pm \sqrt{64h^2 + 16A}}{8}$$ 7. **Simplify the square root expression:** $$x = \frac{-8h \pm 4\sqrt{4h^2 + A}}{8}$$ 8. **Simplify the fraction:** $$x = \frac{-8h}{8} \pm \frac{4\sqrt{4h^2 + A}}{8} = -h \pm \frac{\sqrt{4h^2 + A}}{2}$$ 9. **Final answer:** $$\boxed{x = -h \pm \frac{\sqrt{4h^2 + A}}{2}}$$ This gives two possible values for $$x$$ depending on the $$\pm$$ sign. **Note:** The variables in the answer are $$A$$ and $$h$$, as expected.