Solve a^2(x-5)=25(x-a)

$$a ^ { 2 } ( x - 5 ) = 25 ( x - a )$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply a^{2} by x-5.

$$a^{2}x-5a^{2}=25\left(x-a\right)$$

Use the distributive property to multiply 25 by x-a.

$$a^{2}x-5a^{2}=25x-25a$$

Subtract 25x from both sides.

$$a^{2}x-5a^{2}-25x=-25a$$

Add 5a^{2} to both sides.

$$a^{2}x-25x=-25a+5a^{2}$$

Combine all terms containing x.

$$\left(a^{2}-25\right)x=-25a+5a^{2}$$

The equation is in standard form.

$$\left(a^{2}-25\right)x=5a^{2}-25a$$

Divide both sides by a^{2}-25.

$$\frac{\left(a^{2}-25\right)x}{a^{2}-25}=\frac{5a\left(a-5\right)}{a^{2}-25}$$

Dividing by a^{2}-25 undoes the multiplication by a^{2}-25.

$$x=\frac{5a\left(a-5\right)}{a^{2}-25}$$

Divide 5a\left(-5+a\right) by a^{2}-25.

$$x=\frac{5a}{a+5}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{5a}{a+5}\text{, }&|a|\neq 5\\x\in \mathrm{R}\text{, }&a=5\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a^{2} by x-5.

$$a^{2}x-5a^{2}=25\left(x-a\right)$$

Use the distributive property to multiply 25 by x-a.

$$a^{2}x-5a^{2}=25x-25a$$

Subtract 25x from both sides.

$$a^{2}x-5a^{2}-25x=-25a$$

Add 5a^{2} to both sides.

$$a^{2}x-25x=-25a+5a^{2}$$

Combine all terms containing x.

$$\left(a^{2}-25\right)x=-25a+5a^{2}$$

The equation is in standard form.

$$\left(a^{2}-25\right)x=5a^{2}-25a$$

Divide both sides by a^{2}-25.

$$\frac{\left(a^{2}-25\right)x}{a^{2}-25}=\frac{5a\left(a-5\right)}{a^{2}-25}$$

Dividing by a^{2}-25 undoes the multiplication by a^{2}-25.

$$x=\frac{5a\left(a-5\right)}{a^{2}-25}$$

Divide 5a\left(-5+a\right) by a^{2}-25.

$$x=\frac{5a}{a+5}$$

Solve for a

$$\left\{\begin{matrix}\\a=5\text{, }&\text{unconditionally}\\a=-\frac{5x}{x-5}\text{, }&x\neq 5\end{matrix}\right.$$