Solve x^2+kx+8k+36=0

$$x ^ { 2 } + k x + 8 k + 36 = 0$$

Solve for k

$$k=-\frac{x^{2}+36}{x+8}$$

$$x\neq -8$$

Steps for Solving Linear Equation

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

$$kx+8k+36=-x^{2}$$

Subtract 36 from both sides.

$$kx+8k=-x^{2}-36$$

Combine all terms containing k.

$$\left(x+8\right)k=-x^{2}-36$$

Divide both sides by x+8.

$$\frac{\left(x+8\right)k}{x+8}=\frac{-x^{2}-36}{x+8}$$

Dividing by x+8 undoes the multiplication by x+8.

$$k=\frac{-x^{2}-36}{x+8}$$

Divide -x^{2}-36 by x+8.

$$k=-\frac{x^{2}+36}{x+8}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{\left(k-36\right)\left(k+4\right)}-k}{2}$$

$$x=\frac{-\sqrt{\left(k-36\right)\left(k+4\right)}-k}{2}$$

Solve for x

$$x=\frac{\sqrt{\left(k-36\right)\left(k+4\right)}-k}{2}$$

$$x=\frac{-\sqrt{\left(k-36\right)\left(k+4\right)}-k}{2}\text{, }k\leq -4\text{ or }k\geq 36$$