Answer
$\{3,7\}$.
Work Step by Step
The given expression is
$\Rightarrow 2\sqrt{x-3}+4=x+1$
Subtract $4$ from both sides.
$\Rightarrow 2\sqrt{x-3}+4-4=x+1-4$
Simplify.
$\Rightarrow 2\sqrt{x-3}=x-3$
Square both sides.
$\Rightarrow (2\sqrt{x-3})^2=(x-3)^2$
Use the special formula $(A-B)^2=A^2-2AB+B^2$
We have $A=x$ and $B=3$
$\Rightarrow 4(x-3)=(x)^2-2(x)(3)+(3)^2$
Simplify.
$\Rightarrow 4x-12=x^2-6x+9$
Add $-4x+12$ to both sides.
$\Rightarrow 4x-12-4x+12=x^2-6x+9-4x+12$
Add like terms.
$\Rightarrow 0=x^2-10x+21$
Rewrite the middle term $-10x$ as $-7x-3x$.
$\Rightarrow 0=x^2-7x-3x+21$
Group the terms.
$\Rightarrow 0=(x^2-7x)+(-3x+21)$
Factor each group.
$\Rightarrow 0=x(x-7)-3(x-7)$
Factor out $(x-7)$.
$\Rightarrow 0=(x-7)(x-3)$
$\Rightarrow x-7=0$ or $x-3=0$
Isolate $x$.
$\Rightarrow x=7$ or $x=3$
The solution set is $\{3,7\}$.
