Solve x^2+px-(9p+1)=0

$$x ^ { 2 } + p x - ( 9 p + 1 ) = 0$$

Solve for p

$$p=-\frac{x^{2}-1}{x-9}$$

$$x\neq 9$$

Steps for Solving Linear Equation

To find the opposite of 9p+1, find the opposite of each term.

$$x^{2}+px-9p-1=0$$

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

$$px-9p-1=-x^{2}$$

Add 1 to both sides.

$$px-9p=-x^{2}+1$$

Combine all terms containing p.

$$\left(x-9\right)p=-x^{2}+1$$

The equation is in standard form.

$$\left(x-9\right)p=1-x^{2}$$

Divide both sides by x-9.

$$\frac{\left(x-9\right)p}{x-9}=\frac{1-x^{2}}{x-9}$$

Dividing by x-9 undoes the multiplication by x-9.

$$p=\frac{1-x^{2}}{x-9}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{p^{2}+36p+4}-p}{2}$$

$$x=\frac{-\sqrt{p^{2}+36p+4}-p}{2}$$

Solve for x

$$x=\frac{\sqrt{p^{2}+36p+4}-p}{2}$$

$$x=\frac{-\sqrt{p^{2}+36p+4}-p}{2}\text{, }p\geq 8\sqrt{5}-18\text{ or }p\leq -8\sqrt{5}-18$$