Solve f(x)+5=x^3+5

$$f ( x ) + 5 = x ^ { 3 } + 5$$

Solve for f (complex solution)

$$\left\{\begin{matrix}\\f=x^{2}\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 5 from both sides.

$$fx=x^{3}+5-5$$

Subtract 5 from 5 to get 0.

$$fx=x^{3}$$

The equation is in standard form.

$$xf=x^{3}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{x^{3}}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{x^{3}}{x}$$

Divide x^{3} by x.

$$f=x^{2}$$

Solve for f

$$\left\{\begin{matrix}\\f=x^{2}\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 5 from both sides.

$$fx=x^{3}+5-5$$

Subtract 5 from 5 to get 0.

$$fx=x^{3}$$

The equation is in standard form.

$$xf=x^{3}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{x^{3}}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{x^{3}}{x}$$

Divide x^{3} by x.

$$f=x^{2}$$

Solve for x (complex solution)

$$x=\sqrt{f}$$

$$x=0$$

$$x=-\sqrt{f}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\sqrt{f}\text{; }x=-\sqrt{f}\text{, }&f\geq 0\end{matrix}\right.$$