Solve x^2+a=(x+b)x

$$x ^ { 2 } + a = ( x + b ) x$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply x+b by x.

$$x^{2}+a=x^{2}+bx$$

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

$$x^{2}+bx=x^{2}+a$$

Subtract x^{2} from both sides.

$$bx=x^{2}+a-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$bx=a$$

The equation is in standard form.

$$xb=a$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{a}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{a}{x}$$

Solve for a

$$a=bx$$

Solution Steps

Use the distributive property to multiply x+b by x.

$$x^{2}+a=x^{2}+bx$$

Subtract x^{2} from both sides.

$$a=x^{2}+bx-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$a=bx$$

Solve for b

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

Steps for Solving Linear Equation

Use the distributive property to multiply x+b by x.

$$x^{2}+a=x^{2}+bx$$

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

$$x^{2}+bx=x^{2}+a$$

Subtract x^{2} from both sides.

$$bx=x^{2}+a-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$bx=a$$

The equation is in standard form.

$$xb=a$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{a}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{a}{x}$$