How do you solve #(x - 9) ^ { 2} = 18#?

1 Answer
May 4, 2018

#x=3sqrt2+9,# #-3sqrt2+9#

Explanation:

Solve:

#(x-9)^2=18#

Take the square root of both sides.

#x-9=+-sqrt18#

Prime factorize #18#.

#x-9=+-sqrt(2xx3xx3)#

#x-9=+-sqrt(2xx3^2)#

Apply rule: #sqrt(a^2)=a#

#x-9=+-3sqrt2#

Add #9# to both sides.

#x=+-3sqrt2+9#

#x=3sqrt2+9,# #-3sqrt2+9#