Solve 20x^2+40x_{1}x_{2}=0

$$20 x ^ { 2 } + 40 x _ { 1 } x _ { 2 } = 0$$

Solve for x_1 (complex solution)

$$\left\{\begin{matrix}x_{1}=-\frac{x^{2}}{2x_{2}}\text{, }&x_{2}\neq 0\\x_{1}\in \mathrm{C}\text{, }&x=0\text{ and }x_{2}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 20x^{2} from both sides. Anything subtracted from zero gives its negation.

$$40x_{1}x_{2}=-20x^{2}$$

The equation is in standard form.

$$40x_{2}x_{1}=-20x^{2}$$

Divide both sides by 40x_{2}.

$$\frac{40x_{2}x_{1}}{40x_{2}}=-\frac{20x^{2}}{40x_{2}}$$

Dividing by 40x_{2} undoes the multiplication by 40x_{2}.

$$x_{1}=-\frac{20x^{2}}{40x_{2}}$$

Divide -20x^{2} by 40x_{2}.

$$x_{1}=-\frac{x^{2}}{2x_{2}}$$

Solve for x_1

$$\left\{\begin{matrix}x_{1}=-\frac{x^{2}}{2x_{2}}\text{, }&x_{2}\neq 0\\x_{1}\in \mathrm{R}\text{, }&x=0\text{ and }x_{2}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 20x^{2} from both sides. Anything subtracted from zero gives its negation.

$$40x_{1}x_{2}=-20x^{2}$$

The equation is in standard form.

$$40x_{2}x_{1}=-20x^{2}$$

Divide both sides by 40x_{2}.

$$\frac{40x_{2}x_{1}}{40x_{2}}=-\frac{20x^{2}}{40x_{2}}$$

Dividing by 40x_{2} undoes the multiplication by 40x_{2}.

$$x_{1}=-\frac{20x^{2}}{40x_{2}}$$

Divide -20x^{2} by 40x_{2}.

$$x_{1}=-\frac{x^{2}}{2x_{2}}$$

Solve for x (complex solution)

$$x=-i\sqrt{x_{1}}\sqrt{2x_{2}}$$

$$x=i\sqrt{x_{1}}\sqrt{2x_{2}}$$

Solve for x

$$x=\sqrt{-2x_{1}x_{2}}$$

$$x=-\sqrt{-2x_{1}x_{2}}\text{, }\left(x_{2}\geq 0\text{ and }x_{1}\leq 0\right)\text{ or }\left(x_{1}\geq 0\text{ and }x_{2}\leq 0\right)$$