Answer
$\left\{2,5\right\}$
Work Step by Step
Squaring both sides of the given equation, $
x=\sqrt{7x-10}
,$ results to
\begin{align*}\require{cancel}
(x)^2&=\left(\sqrt{7x-10}\right)^2
\\
x^2&=7x-10
\\
x^2-7x+10&=0
.\end{align*}
Using factoring of trinomials, the equation above is equivalent to
\begin{align*}
(x-2)(x-5)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property) and solving for the variable, then
\begin{array}{l|r}
x-2=0 & x-5=0
\\
x=2 & x=5
.\end{array}
Checking the solutions by substitution in the given equation results to
\begin{array}{l|r}
\text{If }x=2: & \text{If }x=5:
\\\\
2\overset{?}=\sqrt{7(2)-10} & 5\overset{?}=\sqrt{7(5)-10}
\\
2\overset{?}=\sqrt{14-10} & 5\overset{?}=\sqrt{35-10}
\\
2\overset{?}=\sqrt{4} & 5\overset{?}=\sqrt{25}
\\
2\overset{\checkmark}=2 & 5\overset{\checkmark}=5
.\end{array}
Since both solutions satisfy the given equation, then the solution set of the equation $
x=\sqrt{7x-10}
$ is $\left\{2,5\right\}$.
