Answer
The solution is $c=\frac{1}{2}$.
Work Step by Step
The given equation is
$\Rightarrow \sqrt{2c+1}-\sqrt{4c}=0$
Add $\sqrt{4c}$ to each side.
$\Rightarrow \sqrt{2c+1}-\sqrt{4c}+\sqrt{4c}=0+\sqrt{4c}$
Simplify.
$\Rightarrow \sqrt{2c+1}=\sqrt{4c}$
Square each side of the equation.
$\Rightarrow (\sqrt{2c+1})^2=(\sqrt{4c})^2$
Simplify.
$\Rightarrow 2c+1=4c$
Subtract $2c$ from each side.
$\Rightarrow 2c+1-2c=4c-2c$
Simplify.
$\Rightarrow 1=2c$
Divide each side by $2$.
$\Rightarrow \frac{1}{2}=c$
Check $c=\frac{1}{2}$.
$\Rightarrow \sqrt{2c+1}-\sqrt{4c}=0$
$\Rightarrow \sqrt{2(\frac{1}{2})+1}-\sqrt{4(\frac{1}{2})}=0$
$\Rightarrow \sqrt{1+1}-\sqrt{2}=0$
$\Rightarrow \sqrt{2}-\sqrt{2}=0$
$\Rightarrow 0=0$
True.
Hence, the solution is $c=\frac{1}{2}$.
