# Twelve more than the square of a number is seven times the number. How do you find the number?

Nov 15, 2016

The unknown number has the two values of 3 and 4

#### Explanation:

Breaking down the description into its component parts:

Twelve more than: " "->(?_1)+12
the square of a number ->(?_1)^2+12
is " "->(?_1)^2+12=(?_2)
7 times the number " "->(?_1)^2+12=7(?_1)

Let the unknown value be $x$ then we have:

${x}^{2} + 12 = 7 x$

$\implies {x}^{2} - 7 x + 12 = 0$

Note that $3 \times 4 = 12 \text{ and } 3 + 4 = 7$
$\left(x - 3\right) \left(x - 4\right) = 0$
$x = + 3 \text{ and } x = + 4$