Solve x^2-(m+1)x+2=0

$$x ^ { 2 } - ( m + 1 ) x + 2 = 0$$

Solve for m

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

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply m+1 by x.

$$x^{2}-\left(mx+x\right)+2=0$$

To find the opposite of mx+x, find the opposite of each term.

$$x^{2}-mx-x+2=0$$

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

$$-mx-x+2=-x^{2}$$

Add x to both sides.

$$-mx+2=-x^{2}+x$$

Subtract 2 from both sides.

$$-mx=-x^{2}+x-2$$

The equation is in standard form.

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

Divide both sides by -x.

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

Dividing by -x undoes the multiplication by -x.

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

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

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

Solve for x (complex solution)

$$x=\frac{\sqrt{m^{2}+2m-7}+m+1}{2}$$

$$x=\frac{-\sqrt{m^{2}+2m-7}+m+1}{2}$$

Solve for x

$$x=\frac{\sqrt{m^{2}+2m-7}+m+1}{2}$$

$$x=\frac{-\sqrt{m^{2}+2m-7}+m+1}{2}\text{, }m\geq 2\sqrt{2}-1\text{ or }m\leq -2\sqrt{2}-1$$