# Eight more than the square a number is the same as 6 times the number. How do you find the number?

Jan 13, 2017

The number is either $2$ or $4$.

#### Explanation:

From the data, considering the number as $x$, we can write:

${x}^{2} + 8 = 6 x$

Subtract $6 x$ from both sides.

${x}^{2} - 6 x + 8 = 0$

Factorise.

${x}^{2} - 4 x - 2 x + 8 = 0$

$x \left(x - 4\right) - 2 \left(x - 4\right) = 0$

$\left(x - 2\right) \left(x - 4\right) = 0$

$x - 2 = 0$ or $x - 4 = 0$

$x = 2$ or $x = 4$