# Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Exercise Set: 5

$x=1$ and $x=4$

#### Work Step by Step

$\sqrt{9x}=x+2$ Square both sides of the equation: $(\sqrt{9x})^{2}=(x+2)^{2}$ $9x=x^{2}+4x+4$ Take the $9x$ to the right side of the equation and simplify it by combining like terms: $0=x^{2}+4x-9x+4$ $x^{2}-5x+4=0$ Solve this equation by factoring: $(x-1)(x-4)=0$ Set both factors equal to $0$ and solve each individual equation: $x-1=0$ $x=1$ $x-4=0$ $x=4$ Check the answers found by substituting them into the original equation: $x=1$ $\sqrt{9(1)}=1+2$ $3=3$ True $x=4$ $\sqrt{9(4)}=4+2$ $6=6$ True Our two final answers are $x=1$ and $x=4$

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