Solve 2x^3+x^2+kx+2=0

$$2 x ^ { 3 } + x ^ { 2 } + k x + 2 = 0$$

Solve for k

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

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 2x^{3} from both sides. Anything subtracted from zero gives its negation.

$$x^{2}+kx+2=-2x^{3}$$

Subtract x^{2} from both sides.

$$kx+2=-2x^{3}-x^{2}$$

Subtract 2 from both sides.

$$kx=-2x^{3}-x^{2}-2$$

The equation is in standard form.

$$xk=-2x^{3}-x^{2}-2$$

Divide both sides by x.

$$\frac{xk}{x}=\frac{-2x^{3}-x^{2}-2}{x}$$

Dividing by x undoes the multiplication by x.

$$k=\frac{-2x^{3}-x^{2}-2}{x}$$

Divide -2x^{3}-x^{2}-2 by x.

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