Chapter 4 - Quadratic Functions - 4.4 Solving Quadratic Equations by the Square Root Property and Completing the Square - 4.4 Exercises - Page 346: 10

$x=5-\sqrt {41},5+\sqrt {41}$

When taking the square root of a number, you get a positive and a negative answer. $-9(x-5)^2=-369$ $(x-5)^2=41$ $x-5=\sqrt {41}$ $x=5+\sqrt {41}$ or $x-5=-\sqrt {41}$ $x=5-\sqrt {41}$. So $x=5-\sqrt {41},5+\sqrt {41}$.