# How do you solve x^2 - 18x + 74 = 0 by completing the square?

Jun 13, 2016

$x = 9 \pm \sqrt{7}$

#### Explanation:

Complete the square and use the difference of squares identity:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

with $a = \left(x - 9\right)$ and $b = \sqrt{7}$ as follows:

$0 = {x}^{2} - 18 x + 74$

$= {x}^{2} - 18 x + 81 - 7$

$= {\left(x - 9\right)}^{2} - {\left(\sqrt{7}\right)}^{2}$

$= \left(\left(x - 9\right) - \sqrt{7}\right) \left(\left(x - 9\right) + \sqrt{7}\right)$

$= \left(x - 9 - \sqrt{7}\right) \left(x - 9 + \sqrt{7}\right)$

Hence the zeros are:

$x = 9 \pm \sqrt{7}$