Solve 2x^2+kx-1=0

$$2 x ^ { 2 } + k x - 1 = 0$$

Solve for k

$$k=-2x+\frac{1}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$kx-1=-2x^{2}$$

Add 1 to both sides.

$$kx=-2x^{2}+1$$

The equation is in standard form.

$$xk=1-2x^{2}$$

Divide both sides by x.

$$\frac{xk}{x}=\frac{1-2x^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$k=\frac{1-2x^{2}}{x}$$

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

$$k=-2x+\frac{1}{x}$$

Solve for x

$$x=\frac{\sqrt{k^{2}+8}-k}{4}$$

$$x=\frac{-\sqrt{k^{2}+8}-k}{4}$$