Solve m^2x+x=m^3+mx+1

$$m ^ { 2 } x + x = m ^ { 3 } + m x + 1$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=m+1\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&m=\frac{1+\sqrt{3}i}{2}\text{ or }m=\frac{-\sqrt{3}i+1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract mx from both sides.

$$m^{2}x+x-mx=m^{3}+1$$

Combine all terms containing x.

$$\left(m^{2}+1-m\right)x=m^{3}+1$$

The equation is in standard form.

$$\left(m^{2}-m+1\right)x=m^{3}+1$$

Divide both sides by 1-m+m^{2}.

$$\frac{\left(m^{2}-m+1\right)x}{m^{2}-m+1}=\frac{m^{3}+1}{m^{2}-m+1}$$

Dividing by 1-m+m^{2} undoes the multiplication by 1-m+m^{2}.

$$x=\frac{m^{3}+1}{m^{2}-m+1}$$

Divide m^{3}+1 by 1-m+m^{2}.

$$x=m+1$$

Solve for x

$$x=m+1$$

Steps for Solving Linear Equation

Subtract mx from both sides.

$$m^{2}x+x-mx=m^{3}+1$$

Combine all terms containing x.

$$\left(m^{2}+1-m\right)x=m^{3}+1$$

The equation is in standard form.

$$\left(m^{2}-m+1\right)x=m^{3}+1$$

Divide both sides by 1-m+m^{2}.

$$\frac{\left(m^{2}-m+1\right)x}{m^{2}-m+1}=\frac{m^{3}+1}{m^{2}-m+1}$$

Dividing by 1-m+m^{2} undoes the multiplication by 1-m+m^{2}.

$$x=\frac{m^{3}+1}{m^{2}-m+1}$$

Divide m^{3}+1 by 1-m+m^{2}.

$$x=m+1$$

Solve for m (complex solution)

$$m=\frac{-\sqrt{3}i+1}{2}\approx 0.5-0.866025404i$$

$$m=\frac{1+\sqrt{3}i}{2}\approx 0.5+0.866025404i$$

$$m=x-1$$

Solve for m

$$m=x-1$$