Solve x=-frac{sqrt{6}}{3sqrt{2}}

$$x = - \frac { \sqrt { 6 } } { 3 \sqrt { 2 } }$$

Solve for x

$$x=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{\sqrt{6}}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$x=-\frac{\sqrt{6}\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$x=-\frac{\sqrt{6}\sqrt{2}}{3\times 2}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$x=-\frac{\sqrt{2}\sqrt{3}\sqrt{2}}{3\times 2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$x=-\frac{2\sqrt{3}}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$x=-\frac{2\sqrt{3}}{6}$$

Divide 2\sqrt{3} by 6 to get \frac{1}{3}\sqrt{3}.

$$x=-\frac{1}{3}\sqrt{3}$$

Assign x

$$x≔-\frac{\sqrt{3}}{3}$$