## Intermediate Algebra (12th Edition)

$x=-\dfrac{7}{10}$
$\bf{\text{Solution Outline:}}$ To solve the given radical equation, $5\sqrt{4x+1}=3\sqrt{10x+2} ,$ square both sides of the equation and then isolate the variable. Finally, do checking of the solution with the original equation. $\bf{\text{Solution Details:}}$ Squaring both sides of the equation results to \begin{array}{l}\require{cancel} \left( 5\sqrt{4x+1} \right)^2=\left( 3\sqrt{10x+2} \right)^2 \\\\ 25(4x+1)=9(10x+2) .\end{array} Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 25(4x)+25(1)=9(10x)+9(2) \\\\ 100x+25=90x+18 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 100x-90x=18-25 \\\\ 10x=-7 \\\\ x=-\dfrac{7}{10} .\end{array} Upon checking, $x=-\dfrac{7}{10}$ satisfies the original equation.