1. **State the problem:** Solve the equation $\sqrt{a} - 6 + 5 = -10$ for $a$. 2. **Simplify the equation:** Combine like terms on the left side: $$\sqrt{a} - 6 + 5 = \sqrt{a} - 1$$ So the equation becomes: $$\sqrt{a} - 1 = -10$$ 3. **Isolate the square root term:** Add 1 to both sides: $$\sqrt{a} - 1 + 1 = -10 + 1$$ $$\sqrt{a} = -9$$ 4. **Analyze the result:** The square root of a real number $a$ cannot be negative. Since $\sqrt{a} = -9$ is impossible for real $a$, there is no real solution. 5. **Check for extraneous solutions:** The problem's graph and calculations seem to suggest $a=231$, but this contradicts the original equation because $\sqrt{231} \approx 15.2$, and substituting back: $$15.2 - 6 + 5 = 14.2 \neq -10$$ Therefore, the value $a=231$ is not a solution. **Final answer:** There is no real solution to the equation $\sqrt{a} - 6 + 5 = -10$.