How do you solve #sqrt(8-x)=x+6# and identify any restrictions?
The right side cannot be negative and neither can the argument of the radical.
Square both sides.
Solve the quadratic.
Discard any roots that violate the restrictions.
The restrictions are that the right side cannot be negative and the same for the argument of the radical:
Add this restriction to the given equation:
Square both sides:
Combine like terms:
Use the quadratic formula:
The negative root us outside the restriction, therefore, we discard it: