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

1 Answer
Gió
Aug 19, 2015

I found: x=27x=27

Explanation:

I would square both sides to get:
25(x-2)-30sqrt(x-2)+9=19x-2925(x−2)−30√x−2+9=19x−29
25x-50-30sqrt(x-2)+9=19x-2925x−50−30√x−2+9=19x−29 rearranging:
30sqrt(x-2)=25x-50+9-19x+2930√x−2=25x−50+9−19x+29
30sqrt(x-2)=6x-1230√x−2=6x−12 square again:
900(x-2)=36x^2-144x+144900(x−2)=36x2−144x+144
900x-1800=36x^2-144x+144900x−1800=36x2−144x+144
36x^2-1044x+1944=036x2−1044x+1944=0
Use the Quadratic Formula:
x_(1,2)=(1044+-sqrt(1089936-279936))/72=(1044+-900)/72=x1,2=1044±√1089936−27993672=1044±90072=
Two solutions:
x_1=27x1=27
x_2=2x2=2
If you use these values into the original equation only the first works (try it).

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