Solve 2x=sqrt{1-1/sqrt{2}}

$$2x= \sqrt{ 1- \frac{ 1 }{ \sqrt{ 2 } } }$$

Solve for x

$$x=\frac{\sqrt{4-2\sqrt{2}}}{4}\approx 0.27059805$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$2x=\sqrt{1-\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$2x=\sqrt{1-\frac{\sqrt{2}}{2}}$$

The equation is in standard form.

$$2x=\sqrt{-\frac{\sqrt{2}}{2}+1}$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{\sqrt{\sqrt{2}-1}}{2\sqrt[4]{2}}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{\sqrt{\sqrt{2}-1}}{2\sqrt[4]{2}}$$

Divide \frac{\sqrt{\sqrt{2}-1}}{\sqrt[4]{2}} by 2.

$$x=\frac{2^{\frac{3}{4}}\sqrt{\sqrt{2}-1}}{4}$$