How do you solve #sqrt(58n) = 125(n + 4) #?

1 Answer
Nov 9, 2015

You need to square the both parts.
As #sqrt(58n)# is only defined for #n>0#, both parts of your equation are positive, so you can do so safely.

#sqrt(58n) = 125(n+4)#
# 58n = 125^2(n+4)^2#
#58n = 125^2(n^2 + 8n + 16)#

Dividing both sides of the equation by #125^2# yields:
# 58 / 125^2 n = n^2 + 8n + 16 #
#<=>#
# n^2 + (8 - 58/125^2) n + 16 = 0#

This is a regular quadratic equation which can be solved by regular means. The numbers are really ugly though..