# How do you solve (8x-9)^2=6?

Feb 27, 2017

$x = 1.431 \text{ and } x = 0.819$

#### Explanation:

If you had an equation such as ${x}^{2} = 25 ,$

you could solve it easily by taking the square root of both sides:

$x = \pm \sqrt{25} = \pm 5$

The given equation is in exactly the same form:

${\left(8 x - 9\right)}^{2} = 6 \text{ } \leftarrow$ take the square root of both sides

$8 x - 9 = \pm \sqrt{6} \text{ } \leftarrow$ remember there are two roots

$8 x = \pm \sqrt{6} + 9$

This will give us two answers:

$x = \frac{+ \sqrt{6} + 9}{8} \text{ and } x = \frac{- \sqrt{6} + 9}{8}$

$x = 1.431 \text{ and } x = 0.819$