Question 702144
{{{sqrt(x+10)-6/sqrt(x+10)=5}}} is asking for a change of variable with {{{y=sqrt(x+10)}}}
The equation transforms into
{{{y-6/y=5}}}
Multiplying both sides of the equation time {{{y}}},
we do not lose any solution.
Any solution we gain can be eliminated later.
Multiplying both sides of the equation time {{{y}}} we get
{{{y^2-6=5y}}} --> {{{y^2-5y-6=0}}}
Factoring, we get {{{(y-6)(y+1)=0}}}
The solutions to that equation are {{{y=-1}}} and {{{y=6}}}.
They are both solutions of {{{y-6/y=5}}},
but {{{y=sqrt(x+10)}}} is by definition a positive number,
so we eliminate {{{y=-1}}} as a solution.
We continue with {{{sqrt(x+10)=6}}} --> {{{x+10=6^2}}} --> {{{x+10=36}}}
{{{x+10=36}}} --> {{{x=36-10}}} --> {{{highlight(x=26)}}}