1. **State the problem:** Solve the quadratic equation $$4(x + 6)^2 - 50 = 26$$ for all values of $x$ in simplest form. 2. **Isolate the squared term:** Add 50 to both sides to move constants to the right. $$4(x + 6)^2 - 50 + 50 = 26 + 50$$ $$4(x + 6)^2 = 76$$ 3. **Divide both sides by 4 to isolate $(x+6)^2$:** $$\frac{4(x + 6)^2}{\cancel{4}} = \frac{76}{\cancel{4}}$$ $$ (x + 6)^2 = 19 $$ 4. **Take the square root of both sides:** Remember to include both positive and negative roots. $$x + 6 = \pm \sqrt{19}$$ 5. **Solve for $x$ by subtracting 6 from both sides:** $$x = -6 \pm \sqrt{19}$$ **Final answer:** $$x = -6 + \sqrt{19} \quad \text{or} \quad x = -6 - \sqrt{19}$$ This means there are two solutions to the quadratic equation, expressed in simplest radical form.