Solve x^2+(1-p)x-p=0

$$x ^ { 2 } + ( 1 - p ) x - p = 0$$

Solve for p (complex solution)

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

Steps for Solving Linear Equation

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

$$x^{2}+x-px-p=0$$

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

$$x-px-p=-x^{2}$$

Subtract x from both sides.

$$-px-p=-x^{2}-x$$

Combine all terms containing p.

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

Divide both sides by -x-1.

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

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

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

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

$$p=x$$

Solve for p

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

Steps for Solving Linear Equation

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

$$x^{2}+x-px-p=0$$

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

$$x-px-p=-x^{2}$$

Subtract x from both sides.

$$-px-p=-x^{2}-x$$

Combine all terms containing p.

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

Divide both sides by -x-1.

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

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

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

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

$$p=x$$

Solve for x

$$x=p$$

$$x=-1$$