How do you solve x - 9 = sqrt(x - 3)?

1 Answer
Jul 1, 2016

x=12

Explanation:

First you fix the domain of the solutions:

x-3>=0 and x-9>=0

that's x>=9

then you square both members:

(x-9)^2=(sqrt(x-3))^2

that's

x^2-18x+81=x-3

x^2-18x+81-x+3=0

x^2-19x+84=0

x=(19+-sqrt(19^2-4*84))/2

x=(19+-5)/2

x=7 and x=12

but only x=12 belongs to the calculated domain