Answer: x = 27
Solution, showing all steps:
1) equation: [tex] \sqrt{2x+10}-6=2 [/tex]
2) Clear the square root:
=> [tex] \sqrt{2x+10} =2+6[/tex]
=> [tex] \sqrt{2x+10} =8[/tex]
3) Square both sides of the equality:
=> [tex]2x + 10 = 8^2=64[/tex]
4) Clear x:
2x = 64 - 10
2x = 54
x = 54 / 2
x = 27.
5) Verify that this is not a straneous solutio, by replacing the solution in the equation:
[tex] \sqrt{2(27)+10} -6= 2
\sqrt{54+10}-6=2
\sqrt{64} -6=2
8-6=2
2=2[/tex]
