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

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Answer 1 · 2016-05-19T16:24:56

Solution as the primary root is #x=19#

Add #color(blue)(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 #9xx9=81# so trying #(10+9)^2# proves to be the square root. However #(-19)xx(-19)=(+19)xx(+19) = + 361#

#x=+-19#

There is something called the primary root which is always positive

Solution as the primary root is #x=19#