# How do you solve x^2 - 361 = 0?

May 19, 2016

Solution as the primary root is $x = 19$

#### Explanation:

Add $\textcolor{b l u e}{361}$ to both sides

color(brown)(x^2-361color(blue)(+361)" "=" "0color(blue)(+361)

But -361+361=0

${x}^{2} + 0 = 361$

Square root both sides

$\sqrt{{x}^{2}} = \sqrt{361}$

As 361 is in the hundreds then the root involves 10 as 10^2=100 so the root is something like (10+?)^2

The last digit of 361 is 1 and $9 \times 9 = 81$ so trying ${\left(10 + 9\right)}^{2}$ proves to be the square root. However $\left(- 19\right) \times \left(- 19\right) = \left(+ 19\right) \times \left(+ 19\right) = + 361$

$x = \pm 19$

There is something called the primary root which is always positive

Solution as the primary root is $x = 19$