Solve a^2(x-b)=c

$$a ^ { 2 } ( x - b ) = c$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply a^{2} by x-b.

$$a^{2}x-a^{2}b=c$$

Subtract a^{2}x from both sides.

$$-a^{2}b=c-a^{2}x$$

Reorder the terms.

$$-ba^{2}=-xa^{2}+c$$

The equation is in standard form.

$$\left(-a^{2}\right)b=c-xa^{2}$$

Divide both sides by -a^{2}.

$$\frac{\left(-a^{2}\right)b}{-a^{2}}=\frac{c-xa^{2}}{-a^{2}}$$

Dividing by -a^{2} undoes the multiplication by -a^{2}.

$$b=\frac{c-xa^{2}}{-a^{2}}$$

Divide c-xa^{2} by -a^{2}.

$$b=x-\frac{c}{a^{2}}$$

Solve for b

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

Steps for Solving Linear Equation

Use the distributive property to multiply a^{2} by x-b.

$$a^{2}x-a^{2}b=c$$

Subtract a^{2}x from both sides.

$$-a^{2}b=c-a^{2}x$$

Reorder the terms.

$$-ba^{2}=-xa^{2}+c$$

The equation is in standard form.

$$\left(-a^{2}\right)b=c-xa^{2}$$

Divide both sides by -a^{2}.

$$\frac{\left(-a^{2}\right)b}{-a^{2}}=\frac{c-xa^{2}}{-a^{2}}$$

Dividing by -a^{2} undoes the multiplication by -a^{2}.

$$b=\frac{c-xa^{2}}{-a^{2}}$$

Divide c-xa^{2} by -a^{2}.

$$b=x-\frac{c}{a^{2}}$$

Solve for a (complex solution)

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

Solve for a

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