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

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

Solve for a

$$a=x+1+\frac{1}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$x^{2}-\left(ax-x\right)+1=0$$

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

$$x^{2}-ax+x+1=0$$

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

$$-ax+x+1=-x^{2}$$

Subtract x from both sides.

$$-ax+1=-x^{2}-x$$

Subtract 1 from both sides.

$$-ax=-x^{2}-x-1$$

The equation is in standard form.

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

Divide both sides by -x.

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

Dividing by -x undoes the multiplication by -x.

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

Divide -x^{2}-x-1 by -x.

$$a=x+1+\frac{1}{x}$$

Solve for x (complex solution)

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

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

Solve for x

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

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