How do you solve (5- x ) ^ { \frac { 1} { 2} } = ( \frac { x } { 4} ) ^ { \frac { 1} { 2} }?

Dec 12, 2016

Rewrite the equation as $\sqrt{5 - x} = \sqrt{\frac{x}{4}}$

Kind of helps with visualizing what needs to be done next.

Square both sides and get rid of that nasty radical.

Then you have:

$5 - x = \frac{x}{4}$

Multiply both sides by 4 to get rid of that ridiculous rational function.

$20 - 4 x = 4$

Now it looks a little nicer to solve.

$20 - 4 = 4 x$

$\frac{16}{4} = x$

$x = 4$