Solve 64p^2+bp+1=0

$$64 p ^ { 2 } + b p + 1 = 0$$

Solve for b

$$b=-64p-\frac{1}{p}$$

$$p\neq 0$$

Steps for Solving Linear Equation

Subtract 64p^{2} from both sides. Anything subtracted from zero gives its negation.

$$bp+1=-64p^{2}$$

Subtract 1 from both sides.

$$bp=-64p^{2}-1$$

The equation is in standard form.

$$pb=-64p^{2}-1$$

Divide both sides by p.

$$\frac{pb}{p}=\frac{-64p^{2}-1}{p}$$

Dividing by p undoes the multiplication by p.

$$b=\frac{-64p^{2}-1}{p}$$

Divide -64p^{2}-1 by p.

$$b=-64p-\frac{1}{p}$$

Solve for p (complex solution)

$$p=\frac{\sqrt{b^{2}-256}-b}{128}$$

$$p=\frac{-\sqrt{b^{2}-256}-b}{128}$$

Solve for p

$$p=\frac{\sqrt{b^{2}-256}-b}{128}$$

$$p=\frac{-\sqrt{b^{2}-256}-b}{128}\text{, }|b|\geq 16$$