Solve a^2x-2a^2=49x+14a

$$a ^ { 2 } x - 2 a ^ { 2 } = 49 x + 14 a$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{2a}{a-7}\text{, }&a\neq 7\\x\in \mathrm{C}\text{, }&a=-7\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 49x from both sides.

$$a^{2}x-2a^{2}-49x=14a$$

Add 2a^{2} to both sides.

$$a^{2}x-49x=14a+2a^{2}$$

Combine all terms containing x.

$$\left(a^{2}-49\right)x=14a+2a^{2}$$

The equation is in standard form.

$$\left(a^{2}-49\right)x=2a^{2}+14a$$

Divide both sides by a^{2}-49.

$$\frac{\left(a^{2}-49\right)x}{a^{2}-49}=\frac{2a\left(a+7\right)}{a^{2}-49}$$

Dividing by a^{2}-49 undoes the multiplication by a^{2}-49.

$$x=\frac{2a\left(a+7\right)}{a^{2}-49}$$

Divide 2a\left(7+a\right) by a^{2}-49.

$$x=\frac{2a}{a-7}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{2a}{a-7}\text{, }&a\neq 7\\x\in \mathrm{R}\text{, }&a=-7\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 49x from both sides.

$$a^{2}x-2a^{2}-49x=14a$$

Add 2a^{2} to both sides.

$$a^{2}x-49x=14a+2a^{2}$$

Combine all terms containing x.

$$\left(a^{2}-49\right)x=14a+2a^{2}$$

The equation is in standard form.

$$\left(a^{2}-49\right)x=2a^{2}+14a$$

Divide both sides by a^{2}-49.

$$\frac{\left(a^{2}-49\right)x}{a^{2}-49}=\frac{2a\left(a+7\right)}{a^{2}-49}$$

Dividing by a^{2}-49 undoes the multiplication by a^{2}-49.

$$x=\frac{2a\left(a+7\right)}{a^{2}-49}$$

Divide 2a\left(7+a\right) by a^{2}-49.

$$x=\frac{2a}{a-7}$$

Solve for a

$$\left\{\begin{matrix}\\a=-7\text{, }&\text{unconditionally}\\a=\frac{7x}{x-2}\text{, }&x\neq 2\end{matrix}\right.$$