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

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

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=x\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Add x to both sides.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by 1-x.

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

Dividing by 1-x undoes the multiplication by 1-x.

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

Divide x\left(1-x\right) by 1-x.

$$a=x$$

Solve for a

$$\left\{\begin{matrix}\\a=x\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Add x to both sides.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by 1-x.

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

Dividing by 1-x undoes the multiplication by 1-x.

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

Divide x\left(1-x\right) by 1-x.

$$a=x$$

Solve for x

$$x=a$$

$$x=1$$