1. **State the problem:** Solve the quadratic equation $w^2 + 12 - 40 = 0$. 2. **Rewrite the equation:** Simplify the constant terms: $$w^2 + 12 - 40 = w^2 - 28 = 0$$ 3. **Isolate the variable term:** $$w^2 = 28$$ 4. **Take the square root of both sides:** $$w = \pm \sqrt{28}$$ 5. **Simplify the square root:** $$\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}$$ 6. **Final solution:** $$w = \pm 2\sqrt{7}$$ This means $w$ can be either $2\sqrt{7}$ or $-2\sqrt{7}$. **Summary:** We solved the quadratic by isolating $w^2$ and taking the square root, remembering to include both positive and negative roots.