# Chapter 1 - Equations and Inequalities - Exercise Set 1.6 - Page 178: 22

$x=9$

#### Work Step by Step

Isolate the square root on one side. Then square both sides and put all terms on one side. Factor by trial and error to solve for $x$. One of the answers does not work. $\sqrt {x}-3=x-9$ $(\sqrt x)^2=(x-6)^2$ $x=x^2-12x+36$ $x^2-13x+36=0$ $(x-4)(x-9)=0$ $x=4,9$ $\sqrt 4-3\ne4-9$ $x=9$

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