1. **State the problem:** Solve the equation $\sqrt{m - 7} + 18 = 12$ for $m$. 2. **Isolate the square root term:** Subtract 18 from both sides: $$\sqrt{m - 7} + 18 - 18 = 12 - 18$$ $$\sqrt{m - 7} = -6$$ 3. **Analyze the result:** The square root of a real number cannot be negative, so $\sqrt{m - 7} = -6$ has no real solution. 4. **Conclusion:** There is no real value of $m$ that satisfies the original equation. **Note:** The mistake in your work is squaring both sides before isolating the square root term and not recognizing that $\sqrt{m - 7}$ must be non-negative. You should first isolate the square root and check if the right side is non-negative before squaring. **Additional:** For the second equation $\sqrt{45 - 2a} = \sqrt{a - 6}$, you can square both sides safely after ensuring both sides are non-negative. **Summary:** Your approach to squaring was premature and led to an invalid step. Always isolate the square root and check domain restrictions first.