Solve kx^2+16+k=0

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

Solve for k (complex solution)

$$k=-\frac{16}{x^{2}+1}$$

$$x\neq -i\text{ and }x\neq i$$

Steps for Solving Linear Equation

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

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

Combine all terms containing k.

$$\left(x^{2}+1\right)k=-16$$

Divide both sides by x^{2}+1.

$$\frac{\left(x^{2}+1\right)k}{x^{2}+1}=-\frac{16}{x^{2}+1}$$

Dividing by x^{2}+1 undoes the multiplication by x^{2}+1.

$$k=-\frac{16}{x^{2}+1}$$

Solve for k

$$k=-\frac{16}{x^{2}+1}$$

Steps for Solving Linear Equation

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

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

Combine all terms containing k.

$$\left(x^{2}+1\right)k=-16$$

Divide both sides by x^{2}+1.

$$\frac{\left(x^{2}+1\right)k}{x^{2}+1}=-\frac{16}{x^{2}+1}$$

Dividing by x^{2}+1 undoes the multiplication by x^{2}+1.

$$k=-\frac{16}{x^{2}+1}$$

Solve for x (complex solution)

$$x=-\sqrt{-1-\frac{16}{k}}$$

$$x=\sqrt{-1-\frac{16}{k}}\text{, }k\neq 0$$

Solve for x

$$x=\sqrt{-1-\frac{16}{k}}$$

$$x=-\sqrt{-1-\frac{16}{k}}\text{, }k\geq -16\text{ and }k<0$$