how would I solve (x+1)^.5 = (x+6)^.5 -1?

Answer 1

Square both sides:
x+1 = (x+6) - 2√(x+6) + 1
<=> 6 - 2√(x+6) = 0
<=> √(x+6) = 3
<=> x + 6 = 9
<=> x = 3.

Answer 2

(x+1)^.5 = (x+6)^.5 -1

square both sides. (a + b)^2 = a^2 + 2ab + b^2
x + 1 = x+6 - 2(x+6)^.5 + 1

combine like terms
x + 1 = x + 7 - 2(x + 6)^.5

subtract x and 7 for both sides
-6 = -2(x + 6)^.5

divide -2 for both sides
3 = (x + 6)^.5

square both sides
9 = x + 6

subtract 6 for both sides
x = 3

Answer 3

1) Square both side of the equation, then gather terms. Leave the term with (x+6)^(1/2) on the left side.

2) Square both sides of the new equation. You should wind up with something that looks easily solveable.

Good luck!

Answer 4

take the (X+6)^.5 back to the left side. then root it and take the one out..

Answer 5

Square both sides twice.