Solve x^2-(m-1)x+4=0

$$x ^ { 2 } - ( m - 1 ) x + 4 = 0$$

Solve for m

$$m=x+1+\frac{4}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$x^{2}-\left(mx-x\right)+4=0$$

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

$$x^{2}-mx+x+4=0$$

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

$$-mx+x+4=-x^{2}$$

Subtract x from both sides.

$$-mx+4=-x^{2}-x$$

Subtract 4 from both sides.

$$-mx=-x^{2}-x-4$$

The equation is in standard form.

$$\left(-x\right)m=-x^{2}-x-4$$

Divide both sides by -x.

$$\frac{\left(-x\right)m}{-x}=\frac{-x^{2}-x-4}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$m=\frac{-x^{2}-x-4}{-x}$$

Divide -x^{2}-x-4 by -x.

$$m=x+1+\frac{4}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{\left(m-5\right)\left(m+3\right)}+m-1}{2}$$

$$x=\frac{-\sqrt{\left(m-5\right)\left(m+3\right)}+m-1}{2}$$

Solve for x

$$x=\frac{\sqrt{\left(m-5\right)\left(m+3\right)}+m-1}{2}$$

$$x=\frac{-\sqrt{\left(m-5\right)\left(m+3\right)}+m-1}{2}\text{, }m\leq -3\text{ or }m\geq 5$$