Solve kx^2+16=0

$$k x ^ { 2 } + 16 = 0$$

Solve for k

$$k=-\frac{16}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 16 from both sides. Anything subtracted from zero gives its negation.

$$kx^{2}=-16$$

The equation is in standard form.

$$x^{2}k=-16$$

Divide both sides by x^{2}.

$$\frac{x^{2}k}{x^{2}}=-\frac{16}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$k=-\frac{16}{x^{2}}$$

Solve for x (complex solution)

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

$$x=4ik^{-\frac{1}{2}}\text{, }k\neq 0$$

Solve for x

$$x=4\sqrt{-\frac{1}{k}}$$

$$x=-4\sqrt{-\frac{1}{k}}\text{, }k<0$$