Square root of x+8= square root of x-4 then add 2 has several ambiguities, not the least in that you haven't provided the instructions. I'm making the assumption that you want to solve Square root of x+8= square root of x-4 then add 2 for x:
√(x+8) = √(x-4) + 2
Square both sides:
x+8 = (x-4) + 4√(x-4) + 4, or
4 = 4√(x-4) + 4, or 0= 4√(x-4), or 4√(x-4)
= 0,
or
√(x-4) = 0. Squaring both sides, we get x-4=0, so that x=4. It is essential to check solutions; substitute 4 for x in the original problem and determine whether the equation is true or false.
