# How do you solve the inequality x^2+12x<-36?

Nov 6, 2016

No solution.

#### Explanation:

${x}^{2} + 12 x < - 36$

$\Leftrightarrow {x}^{2} + 12 x + 36 < 0$

or ${x}^{2} + 2 \times 6 \times x + {6}^{2} < 0$

or ${\left(x + 6\right)}^{2} < 0$

But we cannot have ${\left(x + 6\right)}^{2} < 0$, as ${\left(x + 6\right)}^{2}$ is always positive.

Hence, we have no solution.