Question 319367
sqrt{5x + 29} = x + 3

Square both sides to begin. By squaring both sides, you will then be able to remove the radical from the left side.

[sqrt{5x + 29}]^2 = (x + 3)^2

5x + 29 = x^2 + 6x + 9


0 = x^2 + 6x - 5x + 9 - 29

0 = x^2 + x - 20

0 = (x - 4)(x + 5)

Set each factor to zero and solve for x.

x - 4 = 0

x = 4

OR

x + 5 = 0

x = -5

To make sure that x = 4 and x = -5 are correct, plug those two values for x into the original radical equation given.  The correct x value will produce the same answer on both sides of the equation after simplifying.  I'll let you do that, however.