Solve x^2-(a+beta)x+abeta=0

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

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=x\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=\beta \end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a+\beta by x.

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

To find the opposite of ax+\beta x, find the opposite of each term.

$$x^{2}-ax-\beta x+a\beta =0$$

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

$$-ax-\beta x+a\beta =-x^{2}$$

Add \beta x to both sides.

$$-ax+a\beta =-x^{2}+\beta x$$

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by -x+\beta .

$$\frac{\left(\beta -x\right)a}{\beta -x}=\frac{x\left(\beta -x\right)}{\beta -x}$$

Dividing by -x+\beta undoes the multiplication by -x+\beta .

$$a=\frac{x\left(\beta -x\right)}{\beta -x}$$

Divide x\left(-x+\beta \right) by -x+\beta .

$$a=x$$

Solve for a

$$\left\{\begin{matrix}\\a=x\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=\beta \end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a+\beta by x.

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

To find the opposite of ax+\beta x, find the opposite of each term.

$$x^{2}-ax-\beta x+a\beta =0$$

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

$$-ax-\beta x+a\beta =-x^{2}$$

Add \beta x to both sides.

$$-ax+a\beta =-x^{2}+\beta x$$

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by -x+\beta .

$$\frac{\left(\beta -x\right)a}{\beta -x}=\frac{x\left(\beta -x\right)}{\beta -x}$$

Dividing by -x+\beta undoes the multiplication by -x+\beta .

$$a=\frac{x\left(\beta -x\right)}{\beta -x}$$

Divide x\left(-x+\beta \right) by -x+\beta .

$$a=x$$

Solve for x

$$x=\beta$$

$$x=a$$