How do you solve #sqrt(2x+1)=x-2#?
Right from the start, you know that any solution you find must satisfy the conditions
#2x+1 >=0 => x>= -1/2# #->#you need to take the square root of a positive number;
#x-2>=0 => x>=2# #->#the square root of a positive number is a positive number.
all in all, you need your valid solution(s) to satisfy the condition
Since the radical term is already isolated on one side of the equation, proceed to square both sides to get
Next, move all your terms on one side of the equation and use the quadratic formula to determine the two solutions of this quadratic equation
This means that you have