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

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

Solve for x

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

$$m\neq \frac{1}{2}$$

Steps for Solving Linear Equation

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

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

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

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

Subtract m from both sides.

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

Add 1 to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 2m-1.

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

Dividing by 2m-1 undoes the multiplication by 2m-1.

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

Solve for m

$$m=\frac{\sqrt{4x^{2}+8x+5}}{2}-x-\frac{1}{2}$$

$$m=-\frac{\sqrt{4x^{2}+8x+5}}{2}-x-\frac{1}{2}$$