Solve 2=r*1/2x^2

$$2 = r \cdot \frac { 1 } { 2 } x ^ { 2 }$$

Solve for r

$$r=\frac{4}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$r\times \frac{1}{2}x^{2}=2$$

The equation is in standard form.

$$\frac{x^{2}}{2}r=2$$

Divide both sides by \frac{1}{2}x^{2}.

$$\frac{2\times \frac{x^{2}}{2}r}{x^{2}}=\frac{2\times 2}{x^{2}}$$

Dividing by \frac{1}{2}x^{2} undoes the multiplication by \frac{1}{2}x^{2}.

$$r=\frac{2\times 2}{x^{2}}$$

Divide 2 by \frac{1}{2}x^{2}.

$$r=\frac{4}{x^{2}}$$

Solve for x

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

$$x=-\frac{2}{\sqrt{r}}\text{, }r>0$$