Solve by completing the square. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.) \[ y^{2}+y-9=0 \] \( y=\square \)

To solve the equation \( y^{2}+y-9=0 \) by completing the square, we first rewrite the equation in a way that allows us to complete the square. 1. Move the constant to the other side: \[ y^{2} + y = 9 \] 2. To complete the square, take half of the coefficient of \( y \) (which is 1), square it (to get \( \left(\frac{1}{2}\right)^2 = \frac{1}{4} \)), and add it to both sides: \[ y^{2} + y + \frac{1}{4} = 9 + \frac{1}{4} \] 3. This gives us: \[ \left( y + \frac{1}{2} \right)^{2} = \frac{36}{4} + \frac{1}{4} = \frac{37}{4} \] 4. Now, take the square root of both sides: \[ y + \frac{1}{2} = \pm \sqrt{\frac{37}{4}} \] 5. Simplifying: \[ y + \frac{1}{2} = \pm \frac{\sqrt{37}}{2} \] 6. Finally, isolate \( y \): \[ y = -\frac{1}{2} \pm \frac{\sqrt{37}}{2} \] So the solutions are: \[ y = \frac{-1 + \sqrt{37}}{2}, \quad y = \frac{-1 - \sqrt{37}}{2} \] Thus, the final answer is: \[ y = \frac{-1 + \sqrt{37}}{2}, \frac{-1 - \sqrt{37}}{2} \]