Question

can someone check my work and help me finish solving this..see attachment

Answer 1

if you square one side u must square the other side too!

Answer 2

(√(x-9) )+(√(5x-14))=7
Take one of the roots to the right hand side
(√(x-9) )=7-(√(5x-14))
Square both the right and left side
(√(x-9) )²= (7-(√(5x-14)))²
x - 9=49 - (14√(5x-14)) + 5x – 14
x-9=35+5x-(14√(5x-14))
Grouping the root on one side and the other variables and constant at the other we have
(14√(5x-14))=35+9+5x-x
Squaring both sides
(14√(5x-14))²=(44+4x)²
196(5x-14)=(44)²+2(44)(4x)+(4x)²
980x-2744=1936+352x+16x²
Summing all based on their variables
1936+2744+352x-980x+16x²=0
16x² - 628x + 1936=0
Solving this simultaneously
x=35.87 or x=3.37