1. Solve the equation $y(y - 2) = 18 + 5y$. 2. Start by expanding the left side: $$y^2 - 2y = 18 + 5y$$ 3. Move all terms to one side to set the equation to zero: $$y^2 - 2y - 18 - 5y = 0$$ 4. Combine like terms: $$y^2 - 7y - 18 = 0$$ 5. Use the quadratic formula $y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ where $a=1$, $b=-7$, and $c=-18$. 6. Calculate the discriminant: $$\Delta = (-7)^2 - 4 \times 1 \times (-18) = 49 + 72 = 121$$ 7. Find the roots: $$y = \frac{-(-7) \pm \sqrt{121}}{2 \times 1} = \frac{7 \pm 11}{2}$$ 8. Calculate each root: - For $+$ sign: $$y = \frac{7 + 11}{2} = \frac{18}{2} = 9$$ - For $-$ sign: $$y = \frac{7 - 11}{2} = \frac{-4}{2} = -2$$ 9. Therefore, the solutions are $y = 9$ or $y = -2$. This matches the given answer. Note: The second equation and graph description are not solved here as per instructions to solve only the first problem.