Solve 4x^2+mx+1=0

$$4 x ^ { 2 } + m x + 1 = 0$$

Solve for m

$$m=-4x-\frac{1}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

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

Subtract 1 from both sides.

$$mx=-4x^{2}-1$$

The equation is in standard form.

$$xm=-4x^{2}-1$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

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

$$m=-4x-\frac{1}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{m^{2}-16}-m}{8}$$

$$x=\frac{-\sqrt{m^{2}-16}-m}{8}$$

Solve for x

$$x=\frac{\sqrt{m^{2}-16}-m}{8}$$

$$x=\frac{-\sqrt{m^{2}-16}-m}{8}\text{, }|m|\geq 4$$