How do you solve #sqrt(2x - 8) = 4 -x#?
Start with a condition for existing of a square root on the left side of an equation:
a condition for the right side of an equation to be non-negative since on the left we have an arithmetic (that is, non-negative) value of a square root:
At this point we can see that these two intervals,
This is a legitimate way to conclude this description in this particular case.
However, we might not notice that
Square both sides of the equation:
To no surprise, we have received a solution
The second solution,
CHECK of the found solution has already been performed above, no need to repeat it here, but, in general, must always be performed.