Solve 0=4x^2+12x+18+2k

$$0 = 4 x ^ { 2 } + 12 x + 18 + 2 k$$

Solve for k

$$k=-2x^{2}-6x-9$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$4x^{2}+12x+18+2k=0$$

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

$$12x+18+2k=-4x^{2}$$

Subtract 12x from both sides.

$$18+2k=-4x^{2}-12x$$

Subtract 18 from both sides.

$$2k=-4x^{2}-12x-18$$

Divide both sides by 2.

$$\frac{2k}{2}=\frac{-4x^{2}-12x-18}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$k=\frac{-4x^{2}-12x-18}{2}$$

Divide -4x^{2}-12x-18 by 2.

$$k=-2x^{2}-6x-9$$

Solve for x (complex solution)

$$x=\frac{\sqrt{-2k-9}-3}{2}$$

$$x=\frac{-\sqrt{-2k-9}-3}{2}$$

Solve for x

$$x=\frac{\sqrt{-2k-9}-3}{2}$$

$$x=\frac{-\sqrt{-2k-9}-3}{2}\text{, }k\leq -\frac{9}{2}$$