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.

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

Subtract x from both sides.

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

Combine all terms containing a.

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

Divide both sides by -1-x.

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

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

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

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.

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

Subtract x from both sides.

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

Combine all terms containing a.

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

Divide both sides by -1-x.

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

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

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

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

$$a=x$$

Solve for x

$$x=a$$

$$x=-1$$