2+square root of 4-x=x
rewrite it as
√(4-x) = x-2
now square both sides
4-x = x^2 - 4x + 4
x(x-3)=0
so x = 0 or x = 3
BUT when we square an equation, all answers must be verified in the original equation
Which answer works and which doesn't?
To verify which answer works and which doesn't, we need to substitute both values of x (0 and 3) back into the original equation:
For x = 0:
2 + √(4 - 0) = 0
2 + √4 = 0
2 + 2 = 0
4 = 0
This equation is not true, so x = 0 is not a valid solution.
For x = 3:
2 + √(4 - 3) = 3
2 + √1 = 3
2 + 1 = 3
3 = 3
This equation is true, so x = 3 is a valid solution.
Therefore, the only solution that works is x = 3.