# Algebra Math Problem: Solve for x when equation in root x

## Find the value of *x*, when root x plus root of x minus root of 1 minus x equals 1

\sqrt x + \sqrt{x-\sqrt{1-x}}=1

x=?

## Solution to the algebra math problem

\sqrt x + \sqrt{x-\sqrt{1-x}}=1

\Rightarrow \sqrt{x-\sqrt{1-x}}=1-\sqrt x

Square both sides then

\Rightarrow (\sqrt{x-\sqrt{1-x}})^2=(1-\sqrt x)^2

\Rightarrow x-\sqrt{1-x}=1-2\sqrt x+x

\Rightarrow -\sqrt{1-x}=1-2\sqrt x

Square both sides again

\Rightarrow (-\sqrt{1-x})^2=(1-2\sqrt x)^2

\Rightarrow 1-x=1-4\sqrt x+4x

\Rightarrow 5x=4\sqrt x

\Rightarrow \sqrt x=\dfrac{5}{4}

\Rightarrow x=\dfrac{25}{16}