# How do you solve 49a^2-1=80?

May 2, 2018

$a = \pm \frac{9}{7}$

#### Explanation:

$49 {a}^{2} - 1 = 80$

$49 {a}^{2} - 81 = 0 \rightarrow$ This is an example of difference of squares

Difference of squares: ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

$\left(7 a + 9\right) \left(7 a - 9\right) = 0$

$7 a + 9 = 0$

$7 a = - 9$

$a = - \frac{9}{7}$

$7 a - 9 = 0$

$7 a = 9$

$a = \frac{9}{7}$