Solve y=ax^2+5x^2

$$y = a x ^ { 2 } + 5 x ^ { 2 }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-5+\frac{y}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax^{2}+5x^{2}=y$$

Subtract 5x^{2} from both sides.

$$ax^{2}=y-5x^{2}$$

The equation is in standard form.

$$x^{2}a=y-5x^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{y-5x^{2}}{x^{2}}$$

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

$$a=\frac{y-5x^{2}}{x^{2}}$$

Divide y-5x^{2} by x^{2}.

$$a=-5+\frac{y}{x^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=-5+\frac{y}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax^{2}+5x^{2}=y$$

Subtract 5x^{2} from both sides.

$$ax^{2}=y-5x^{2}$$

The equation is in standard form.

$$x^{2}a=y-5x^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{y-5x^{2}}{x^{2}}$$

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

$$a=\frac{y-5x^{2}}{x^{2}}$$

Divide y-5x^{2} by x^{2}.

$$a=-5+\frac{y}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\left(a+5\right)^{-\frac{1}{2}}\sqrt{y}\text{; }x=\left(a+5\right)^{-\frac{1}{2}}\sqrt{y}\text{, }&a\neq -5\\x\in \mathrm{C}\text{, }&y=0\text{ and }a=-5\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{\frac{y}{a+5}}\text{; }x=-\sqrt{\frac{y}{a+5}}\text{, }&\left(y\geq 0\text{ and }a>-5\right)\text{ or }\left(y\leq 0\text{ and }a<-5\right)\\x\in \mathrm{R}\text{, }&y=0\text{ and }a=-5\end{matrix}\right.$$