how do you solve square root of 7x+2 equals 2x?

Answer 1

sqrt(7x + 2) = 2x

Square both sides:
7x + 2 = (2x)^2
7x + 2 = 4x^2

Subtract both sides by 7x+2
4x^2 - 7x - 2 = 0

Factor:
(4x + 1)(x - 2) = 0

4x + 1 = 0
x = -1/4

x - 2 = 0
x = 2


Check answers:
sqrt(7(-1/4) + 2) = 2(-1/4)
sqrt(1/4) = -1/2
-1/2 = -1/2

sqrt(7(2) + 2) = 2(2)
sqrt(16) = 4
4 = 4

Both answers check.
x = -1/4 or 2

Answer 2

sqrt(7x+2) = 2x ---> square both sides

7x + 2 = 4x^2

0 = 4x^2 - 7x -2

0 = (4x+1)(x-2)

x = -1/4, 2