Solve x^2-ax+b=0

$$x ^ { 2 } - a x + b = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=x+\frac{b}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&b=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Subtract b from both sides.

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

The equation is in standard form.

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

Divide both sides by -x.

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

Dividing by -x undoes the multiplication by -x.

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

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

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

Solve for a

$$\left\{\begin{matrix}a=x+\frac{b}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&b=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

Subtract b from both sides.

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

The equation is in standard form.

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

Divide both sides by -x.

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

Dividing by -x undoes the multiplication by -x.

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

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

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

Solve for b

$$b=-x\left(x-a\right)$$

Solution Steps

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

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

Add ax to both sides.

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