Solve x^2+Mx+n=0

$$x ^ { 2 } + M x + n = 0$$

Solve for M (complex solution)

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

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$Mx+n=-x^{2}$$

Subtract n from both sides.

$$Mx=-x^{2}-n$$

The equation is in standard form.

$$xM=-x^{2}-n$$

Divide both sides by x.

$$\frac{xM}{x}=\frac{-x^{2}-n}{x}$$

Dividing by x undoes the multiplication by x.

$$M=\frac{-x^{2}-n}{x}$$

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

$$M=-x-\frac{n}{x}$$

Solve for M

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

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$Mx+n=-x^{2}$$

Subtract n from both sides.

$$Mx=-x^{2}-n$$

The equation is in standard form.

$$xM=-x^{2}-n$$

Divide both sides by x.

$$\frac{xM}{x}=\frac{-x^{2}-n}{x}$$

Dividing by x undoes the multiplication by x.

$$M=\frac{-x^{2}-n}{x}$$

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

$$M=-x-\frac{n}{x}$$

Solve for n

$$n=-x\left(x+M\right)$$

Solution Steps

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$Mx+n=-x^{2}$$

Subtract Mx from both sides.

$$n=-x^{2}-Mx$$