Solve x^2+kx+30=0

$$x ^ { 2 } + k x + 30 = 0$$

Solve for k

$$k=-x-\frac{30}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$kx+30=-x^{2}$$

Subtract 30 from both sides.

$$kx=-x^{2}-30$$

The equation is in standard form.

$$xk=-x^{2}-30$$

Divide both sides by x.

$$\frac{xk}{x}=\frac{-x^{2}-30}{x}$$

Dividing by x undoes the multiplication by x.

$$k=\frac{-x^{2}-30}{x}$$

Divide -x^{2}-30 by x.

$$k=-x-\frac{30}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{k^{2}-120}-k}{2}$$

$$x=\frac{-\sqrt{k^{2}-120}-k}{2}$$

Solve for x

$$x=\frac{\sqrt{k^{2}-120}-k}{2}$$

$$x=\frac{-\sqrt{k^{2}-120}-k}{2}\text{, }|k|\geq 2\sqrt{30}$$