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

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

Solve for a

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

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

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

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

Add x to both sides.

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

Subtract 2 from both sides.

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

The equation is in standard form.

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

Divide both sides by x.

$$\frac{xa}{x}=\frac{-x^{2}+x-2}{x}$$

Dividing by x undoes the multiplication by x.

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

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

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

Solve for x (complex solution)

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

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

Solve for x

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

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