Solve x^2-(p+5)x+36=0

$$x ^ { 2 } - ( p + 5 ) x + 36 = 0$$

Solve for p

$$p=x-5+\frac{36}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply p+5 by x.

$$x^{2}-\left(px+5x\right)+36=0$$

To find the opposite of px+5x, find the opposite of each term.

$$x^{2}-px-5x+36=0$$

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

$$-px-5x+36=-x^{2}$$

Add 5x to both sides.

$$-px+36=-x^{2}+5x$$

Subtract 36 from both sides.

$$-px=-x^{2}+5x-36$$

The equation is in standard form.

$$\left(-x\right)p=-x^{2}+5x-36$$

Divide both sides by -x.

$$\frac{\left(-x\right)p}{-x}=\frac{-x^{2}+5x-36}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$p=\frac{-x^{2}+5x-36}{-x}$$

Divide 5x-x^{2}-36 by -x.

$$p=x-5+\frac{36}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{\left(p-7\right)\left(p+17\right)}+p+5}{2}$$

$$x=\frac{-\sqrt{\left(p-7\right)\left(p+17\right)}+p+5}{2}$$

Solve for x

$$x=\frac{\sqrt{\left(p-7\right)\left(p+17\right)}+p+5}{2}$$

$$x=\frac{-\sqrt{\left(p-7\right)\left(p+17\right)}+p+5}{2}\text{, }p\leq -17\text{ or }p\geq 7$$