Areteem: Math Challenge Three 3.26 Algebra

Online Course Discussion Forum

This is the question:

Find the real roots of \[ x + \sqrt{x+\frac{1}{2} + \sqrt{x + \frac{1}{4}}}=4. \]

Here is a hint: use the following change of variables: $y=\sqrt{x + \dfrac{1}{4}}$. Then $x=y^2 - \dfrac{1}{4}$.