Solve mx^2+1=9-mx^2

$$m x ^ { 2 } + 1 = 9 - m x ^ { 2 }$$

Solve for m

$$m=\frac{4}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Add mx^{2} to both sides.

$$mx^{2}+1+mx^{2}=9$$

Combine mx^{2} and mx^{2} to get 2mx^{2}.

$$2mx^{2}+1=9$$

Subtract 1 from both sides.

$$2mx^{2}=9-1$$

Subtract 1 from 9 to get 8.

$$2mx^{2}=8$$

The equation is in standard form.

$$2x^{2}m=8$$

Divide both sides by 2x^{2}.

$$\frac{2x^{2}m}{2x^{2}}=\frac{8}{2x^{2}}$$

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

$$m=\frac{8}{2x^{2}}$$

Divide 8 by 2x^{2}.

$$m=\frac{4}{x^{2}}$$

Solve for x (complex solution)

$$x=-2m^{-\frac{1}{2}}$$

$$x=2m^{-\frac{1}{2}}\text{, }m\neq 0$$

Solve for x

$$x=\frac{2}{\sqrt{m}}$$

$$x=-\frac{2}{\sqrt{m}}\text{, }m>0$$