Solve Fx=1/3x^2

$$F x = \frac { 1 } { 3 x ^ { 2 } }$$

Solve for F

$$F=\frac{1}{3x^{3}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3x^{2}.

$$Fx\times 3x^{2}=1$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$Fx^{3}\times 3=1$$

The equation is in standard form.

$$3x^{3}F=1$$

Divide both sides by 3x^{3}.

$$\frac{3x^{3}F}{3x^{3}}=\frac{1}{3x^{3}}$$

Dividing by 3x^{3} undoes the multiplication by 3x^{3}.

$$F=\frac{1}{3x^{3}}$$

Solve for x (complex solution)

$$x=\frac{3^{\frac{2}{3}}e^{\frac{2\pi i}{3}}F^{-\frac{1}{3}}}{3}$$

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

$$x=\frac{3^{\frac{2}{3}}e^{\frac{4\pi i}{3}}F^{-\frac{1}{3}}}{3}\text{, }F\neq 0$$

Solve for x

$$x=\frac{3^{\frac{2}{3}}}{3\sqrt[3]{F}}$$

$$F\neq 0$$