How do you solve #5sqrt(x - 2) - 3 =sqrt(19x - 29)#?

1 Answer
Gió
Aug 19, 2015

I found: #x=27#

Explanation:

I would square both sides to get:
#25(x-2)-30sqrt(x-2)+9=19x-29#
#25x-50-30sqrt(x-2)+9=19x-29# rearranging:
#30sqrt(x-2)=25x-50+9-19x+29#
#30sqrt(x-2)=6x-12# square again:
#900(x-2)=36x^2-144x+144#
#900x-1800=36x^2-144x+144#
#36x^2-1044x+1944=0#
Use the Quadratic Formula:
#x_(1,2)=(1044+-sqrt(1089936-279936))/72=(1044+-900)/72=#
Two solutions:
#x_1=27#
#x_2=2#
If you use these values into the original equation only the first works (try it).

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