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

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

Solve for m

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

$$x\neq 1$$

Steps for Solving Linear Equation

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

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

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

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

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

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

Subtract x^{2} from both sides.

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

Subtract 2x from both sides.

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

Combine all terms containing m.

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

The equation is in standard form.

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

Divide both sides by -2x+2.

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

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

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

Divide -\left(x+1\right)^{2} by -2x+2.

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

Solve for x (complex solution)

$$x=\sqrt{m\left(m-4\right)}+m-1$$

$$x=-\sqrt{m\left(m-4\right)}+m-1$$

Solve for x

$$x=\sqrt{m\left(m-4\right)}+m-1$$

$$x=-\sqrt{m\left(m-4\right)}+m-1\text{, }m\geq 4\text{ or }m\leq 0$$