Verified answer

√5x + 1 - √x = 5

Square both sides so you can eliminate the square root sign.

5x + 1 - x = 25

4x + 1 = 25

4x = 24

x = 6

Isolate one of the square roots:

√(5x + 1) = √(x) + 5

Square both sides to cancel off the square root:

5x + 1 = [√x + 5]^2

Expand the brackets:

5x + 1 = x + 10√x + 25

Isolate the square root:

4x - 24 = 10√x

Divide both sides by 2 to simplify the equation:

2x - 12 = 5√x

Square both sides to cancel off the square root:

(2x - 12)^2 = 25x

Expand the brackets:

4x^2 - 48x + 144 = 25x

Move everything to one side:

4x^2 - 73x + 144 = 0

Factor it out:

(4x - 9)(x - 16) = 0

x = 9/4, 16

Always check your solutions whenever you square both sides because sometimes a false/extraneous solution is created. Notice how 9/4 as a solution doesn't match the equation (2 = 5). Therefore 9/4 is NOT a valid solution.

x = 16