Solve y=(m+2)x^2

$$y = ( m + 2 ) x ^ { 2 }$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-2+\frac{y}{x^{2}}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m+2 by x^{2}.

$$y=mx^{2}+2x^{2}$$

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

$$mx^{2}+2x^{2}=y$$

Subtract 2x^{2} from both sides.

$$mx^{2}=y-2x^{2}$$

The equation is in standard form.

$$x^{2}m=y-2x^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}m}{x^{2}}=\frac{y-2x^{2}}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$m=\frac{y-2x^{2}}{x^{2}}$$

Divide y-2x^{2} by x^{2}.

$$m=-2+\frac{y}{x^{2}}$$

Solve for m

$$\left\{\begin{matrix}m=-2+\frac{y}{x^{2}}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m+2 by x^{2}.

$$y=mx^{2}+2x^{2}$$

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

$$mx^{2}+2x^{2}=y$$

Subtract 2x^{2} from both sides.

$$mx^{2}=y-2x^{2}$$

The equation is in standard form.

$$x^{2}m=y-2x^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}m}{x^{2}}=\frac{y-2x^{2}}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$m=\frac{y-2x^{2}}{x^{2}}$$

Divide y-2x^{2} by x^{2}.

$$m=-2+\frac{y}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\left(m+2\right)^{-\frac{1}{2}}\sqrt{y}\text{; }x=\left(m+2\right)^{-\frac{1}{2}}\sqrt{y}\text{, }&m\neq -2\\x\in \mathrm{C}\text{, }&y=0\text{ and }m=-2\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{\frac{y}{m+2}}\text{; }x=-\sqrt{\frac{y}{m+2}}\text{, }&\left(y\geq 0\text{ and }m>-2\right)\text{ or }\left(y\leq 0\text{ and }m<-2\right)\\x\in \mathrm{R}\text{, }&y=0\text{ and }m=-2\end{matrix}\right.$$