Solve bx^2+9-x^2-9b=0

$$b x ^ { 2 } + 9 - x ^ { 2 } - 9 b = 0$$

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=1\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&x=-3\text{ or }x=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$bx^{2}-x^{2}-9b=-9$$

Add x^{2} to both sides.

$$bx^{2}-9b=-9+x^{2}$$

Combine all terms containing b.

$$\left(x^{2}-9\right)b=-9+x^{2}$$

The equation is in standard form.

$$\left(x^{2}-9\right)b=x^{2}-9$$

Divide both sides by x^{2}-9.

$$\frac{\left(x^{2}-9\right)b}{x^{2}-9}=\frac{x^{2}-9}{x^{2}-9}$$

Dividing by x^{2}-9 undoes the multiplication by x^{2}-9.

$$b=\frac{x^{2}-9}{x^{2}-9}$$

Divide x^{2}-9 by x^{2}-9.

$$b=1$$

Solve for b

$$\left\{\begin{matrix}\\b=1\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&|x|=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$bx^{2}-x^{2}-9b=-9$$

Add x^{2} to both sides.

$$bx^{2}-9b=-9+x^{2}$$

Combine all terms containing b.

$$\left(x^{2}-9\right)b=-9+x^{2}$$

The equation is in standard form.

$$\left(x^{2}-9\right)b=x^{2}-9$$

Divide both sides by x^{2}-9.

$$\frac{\left(x^{2}-9\right)b}{x^{2}-9}=\frac{x^{2}-9}{x^{2}-9}$$

Dividing by x^{2}-9 undoes the multiplication by x^{2}-9.

$$b=\frac{x^{2}-9}{x^{2}-9}$$

Divide x^{2}-9 by x^{2}-9.

$$b=1$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=3\text{; }x=-3\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&b=1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=3\text{; }x=-3\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&b=1\end{matrix}\right.$$