# When a number x is added to its square, the total is 12. How do you find two possible values for x?

Apr 10, 2018

$x = - 3 , 4$

#### Explanation:

${x}^{2} + x = 12 \rightarrow$ Subtract 12 from each side

${x}^{2} + x - 12 \rightarrow$ This equation is in standard form: $a {x}^{2} + b x + c$

To solve this, we can graph, use the quadratic formula, or use the "big X" method (I'll use the third)

Think of two numbers that multiply to $c$ (in this case, -12) and add up to $a \cdot b$ (in this case, 1): $- 3 \mathmr{and} 4$

$\left(x - 3\right) \left(x + 4\right) = 0$

$x - 3 = 0$

$x = 3$

$x + 4 = 0$

$x = - 4$