Question

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

Answer 1

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).