## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x=\{-1,2\}$
Isolating the radical expression, the given expression is equivalent to \begin{array}{l}\require{cancel} x=\sqrt{3x+3}-1 \\\\ x+1=\sqrt{3x+3} .\end{array} Squaring both sides, the equation above is equivalent to \begin{array}{l}\require{cancel} x+1=\sqrt{3x+3} \\\\ (x+1)^2=(\sqrt{3x+3})^2 \\\\ (x)^2+2(x)(1)+(1)^2=3x+3 \\\\ x^2+2x+1=3x+3 \\\\ x^2+2x-3x+1-3=0 \\\\ x^2-x-2=0 .\end{array} Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the equation above is equivalent to\begin{array}{l}\require{cancel} x^2-x-2=0 \\\\ (x-2)(x+1)=0 .\end{array} Equating each factor to zero (Zero Product Property) and solving for the variable, then the solutions are $x=\{-1,2\} .$ Upon checking, both solutions, $x=\{-1,2\} ,$ satisfy the original equation.