# The square of a number plus the number is 12. What is the number?

Dec 11, 2016

$x = - 4$ or $x = 3$

#### Explanation:

If $x$ represents the number, then we can express the given information as:

${x}^{2} + x = 12$

Subtract $12$ from both sides to get a quadratic equation in standard form:

${x}^{2} + x - 12 = 0$

Note that $4 \cdot 3 = 12$ and $4 - 3 = 1$. So we find:

$\left(x + 4\right) \left(x - 3\right) = {x}^{2} + x - 12 = 0$

Hence $x = - 4$ or $x = 3$