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

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

Solve for m

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

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2m-1 by x.

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

To find the opposite of 2mx-x, find the opposite of each term.

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

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

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

Subtract x from both sides.

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

Subtract 2 from both sides.

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

The equation is in standard form.

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

Divide both sides by -2x.

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

Dividing by -2x undoes the multiplication by -2x.

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

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

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

Solve for x (complex solution)

$$x=\frac{\sqrt{4m^{2}-4m-7}}{2}+m-\frac{1}{2}$$

$$x=-\frac{\sqrt{4m^{2}-4m-7}}{2}+m-\frac{1}{2}$$

Solve for x

$$x=\frac{\sqrt{4m^{2}-4m-7}}{2}+m-\frac{1}{2}$$

$$x=-\frac{\sqrt{4m^{2}-4m-7}}{2}+m-\frac{1}{2}\text{, }m\geq \sqrt{2}+\frac{1}{2}\text{ or }m\leq \frac{1}{2}-\sqrt{2}$$