Solve ax^2-16y^2=144

$$a x ^ { 2 } - 16 y ^ { 2 } = 144$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{16\left(y^{2}+9\right)}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&\left(y=3i\text{ or }y=-3i\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 16y^{2} to both sides.

$$ax^{2}=144+16y^{2}$$

The equation is in standard form.

$$x^{2}a=16y^{2}+144$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{16y^{2}+144}{x^{2}}$$

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

$$a=\frac{16y^{2}+144}{x^{2}}$$

Divide 144+16y^{2} by x^{2}.

$$a=\frac{16\left(y^{2}+9\right)}{x^{2}}$$

Solve for a

$$a=\frac{16\left(y^{2}+9\right)}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Add 16y^{2} to both sides.

$$ax^{2}=144+16y^{2}$$

The equation is in standard form.

$$x^{2}a=16y^{2}+144$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{16y^{2}+144}{x^{2}}$$

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

$$a=\frac{16y^{2}+144}{x^{2}}$$

Divide 144+16y^{2} by x^{2}.

$$a=\frac{16\left(y^{2}+9\right)}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-4ia^{-\frac{1}{2}}\sqrt{-y^{2}-9}\text{; }x=4ia^{-\frac{1}{2}}\sqrt{-y^{2}-9}\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&\left(y=3i\text{ or }y=-3i\right)\text{ and }a=0\end{matrix}\right.$$

Solve for x

$$x=4\sqrt{\frac{y^{2}+9}{a}}$$

$$x=-4\sqrt{\frac{y^{2}+9}{a}}\text{, }a>0$$