Answer
$\{2,6\}$.
Work Step by Step
The given expression is
$\Rightarrow 2\sqrt{4x+1}-9=x-5$
Add $9$ to both sides.
$\Rightarrow 2\sqrt{4x+1}-9+9=x-5+9$
Simplify.
$\Rightarrow 2\sqrt{4x+1}=x+4$
Square both sides.
$\Rightarrow (2\sqrt{4x+1})^2=(x+4)^2$
Use the special formula $(A-B)^2=A^2-2AB+B^2$
We have $A=x$ and $B=4$
$\Rightarrow 4(4x+1)=(x)^2+2(x)(4)+(4)^2$
Simplify.
$\Rightarrow 16x+4=x^2+8x+16$
Add $-16x-4$ to both sides.
$\Rightarrow 16x+4-16x-4=x^2+8x+16-16x-4$
Add like terms.
$\Rightarrow 0=x^2-8x+12$
Rewrite the middle term $-8x$ as $-6x-2x$.
$\Rightarrow 0=x^2-6x-2x+12$
Group the terms.
$\Rightarrow 0=(x^2-6x)+(-2x+12)$
Factor each group.
$\Rightarrow 0=x(x-6)-2(x-6)$
Factor out $(x-6)$.
$\Rightarrow 0=(x-6)(x-2)$
$\Rightarrow x-6=0$ or $x-2=0$
Isolate $x$.
$\Rightarrow x=6$ or $x=2$
The solution set is $\{2,6\}$.
