Solve x^2-31n+180=0

$$x ^ { 2 } - 31 n + 180 = 0$$

Solve for n

$$n=\frac{x^{2}+180}{31}$$

Steps for Solving Linear Equation

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

$$-31n+180=-x^{2}$$

Subtract 180 from both sides.

$$-31n=-x^{2}-180$$

Divide both sides by -31.

$$\frac{-31n}{-31}=\frac{-x^{2}-180}{-31}$$

Dividing by -31 undoes the multiplication by -31.

$$n=\frac{-x^{2}-180}{-31}$$

Divide -x^{2}-180 by -31.

$$n=\frac{x^{2}+180}{31}$$

Solve for x (complex solution)

$$x=-\sqrt{31n-180}$$

$$x=\sqrt{31n-180}$$

Solve for x

$$x=\sqrt{31n-180}$$

$$x=-\sqrt{31n-180}\text{, }n\geq \frac{180}{31}$$