1. **State the problem:** Simplify the expression and solve the equation: $$m - 1 + 2\sqrt{m} + 4 + m - 1 = 1$$ 2. **Combine like terms:** Group the terms involving $m$ and constants: $$m + m - 1 - 1 + 4 + 2\sqrt{m} = 1$$ Simplify the constants: $$2m + 2 + 2\sqrt{m} = 1$$ 3. **Isolate terms:** Move constants to the right side: $$2m + 2\sqrt{m} = 1 - 2$$ $$2m + 2\sqrt{m} = -1$$ 4. **Divide entire equation by 2:** $$m + \sqrt{m} = -\frac{1}{2}$$ 5. **Analyze the equation:** Since $m$ and $\sqrt{m}$ are real numbers, and $\sqrt{m}$ is defined only for $m \geq 0$, the left side is always non-negative or zero, but the right side is negative. 6. **Conclusion:** There is no real solution to the equation because the left side cannot be negative while the right side is $-\frac{1}{2}$. **Final answer:** No real solution exists for the given equation.