Factor out the common term \(2\).
\[3=\sqrt{2(x+1)}+5\]
Separate terms with roots from terms without roots.
\[3-5=\sqrt{2(x+1)}\]
Simplify \(3-5\) to \(-2\).
\[-2=\sqrt{2(x+1)}\]
Square both sides.
\[4=2(x+1)\]
Divide both sides by \(2\).
\[\frac{4}{2}=x+1\]
Simplify \(\frac{4}{2}\) to \(2\).
\[2=x+1\]
Subtract \(1\) from both sides.
\[2-1=x\]
Simplify \(2-1\) to \(1\).
\[1=x\]
Switch sides.
\[x=1\]
Check solution
When \(x=1\), the original equation \(3=\sqrt{2x+2}+5\) does not hold true.We will drop \(x=1\) from the solution set.
Therefore,
[No Solution]
