Solve sqrt{1/2}x=x

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

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

Express \frac{\sqrt{2}}{2}x as a single fraction.

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

Subtract x from both sides.

$$\frac{\sqrt{2}x}{2}-x=0$$

Multiply both sides of the equation by 2.

$$\sqrt{2}x-2x=0$$

Combine all terms containing x.

$$\left(\sqrt{2}-2\right)x=0$$

Divide 0 by \sqrt{2}-2.

$$x=0$$