Solve y=-1/8x^2quadE

$$y = - \frac { 1 } { 8 } x ^ { 2 } \quad E$$

Solve for E (complex solution)

$$\left\{\begin{matrix}E=-\frac{8y}{x^{2}}\text{, }&x\neq 0\\E\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-\frac{1}{8}x^{2}E=y$$

The equation is in standard form.

$$\left(-\frac{x^{2}}{8}\right)E=y$$

Divide both sides by -\frac{1}{8}x^{2}.

$$\frac{\left(-\frac{x^{2}}{8}\right)E}{-\frac{x^{2}}{8}}=\frac{y}{-\frac{x^{2}}{8}}$$

Dividing by -\frac{1}{8}x^{2} undoes the multiplication by -\frac{1}{8}x^{2}.

$$E=\frac{y}{-\frac{x^{2}}{8}}$$

Divide y by -\frac{1}{8}x^{2}.

$$E=-\frac{8y}{x^{2}}$$

Solve for E

$$\left\{\begin{matrix}E=-\frac{8y}{x^{2}}\text{, }&x\neq 0\\E\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-\frac{1}{8}x^{2}E=y$$

The equation is in standard form.

$$\left(-\frac{x^{2}}{8}\right)E=y$$

Divide both sides by -\frac{1}{8}x^{2}.

$$\frac{\left(-\frac{x^{2}}{8}\right)E}{-\frac{x^{2}}{8}}=\frac{y}{-\frac{x^{2}}{8}}$$

Dividing by -\frac{1}{8}x^{2} undoes the multiplication by -\frac{1}{8}x^{2}.

$$E=\frac{y}{-\frac{x^{2}}{8}}$$

Divide y by -\frac{1}{8}x^{2}.

$$E=-\frac{8y}{x^{2}}$$

Solve for x (complex solution)

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

Solve for x

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