Solve 2x+3x=sqrt{1/2}

$$2x+3x = \sqrt{ \frac{ 1 }{ 2 } }$$

Solve for x

$$x=\frac{\sqrt{2}}{10}\approx 0.141421356$$

Steps for Solving Linear Equation

Combine 2x and 3x to get 5x.

$$5x=\sqrt{\frac{1}{2}}$$

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

$$5x=\frac{\sqrt{1}}{\sqrt{2}}$$

Calculate the square root of 1 and get 1.

$$5x=\frac{1}{\sqrt{2}}$$

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

$$5x=\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$5x=\frac{\sqrt{2}}{2}$$

Multiply both sides of the equation by 2.

$$10x=\sqrt{2}$$

Divide both sides by 10.

$$\frac{10x}{10}=\frac{\sqrt{2}}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$x=\frac{\sqrt{2}}{10}$$