Solve 4x^2+(p-2)x+1=0

$$4 x ^ { 2 } + ( p - 2 ) x + 1 = 0$$

Solve for p

$$p=-4x+2-\frac{1}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply p-2 by x.

$$4x^{2}+px-2x+1=0$$

Subtract 4x^{2} from both sides. Anything subtracted from zero gives its negation.

$$px-2x+1=-4x^{2}$$

Add 2x to both sides.

$$px+1=-4x^{2}+2x$$

Subtract 1 from both sides.

$$px=-4x^{2}+2x-1$$

The equation is in standard form.

$$xp=-4x^{2}+2x-1$$

Divide both sides by x.

$$\frac{xp}{x}=\frac{-4x^{2}+2x-1}{x}$$

Dividing by x undoes the multiplication by x.

$$p=\frac{-4x^{2}+2x-1}{x}$$

Divide -4x^{2}+2x-1 by x.

$$p=-4x+2-\frac{1}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{\left(p-6\right)\left(p+2\right)}-p+2}{8}$$

$$x=\frac{-\sqrt{\left(p-6\right)\left(p+2\right)}-p+2}{8}$$

Solve for x

$$x=\frac{\sqrt{\left(p-6\right)\left(p+2\right)}-p+2}{8}$$

$$x=\frac{-\sqrt{\left(p-6\right)\left(p+2\right)}-p+2}{8}\text{, }p\leq -2\text{ or }p\geq 6$$