4+sqrt(4+x^2)=x, I need to isolate the x variable in the radical equation, but I can't figure out how to do it.

Question

The answer is x=3/2

Answer 1

4+sqrt(4+x^2)=x

sqrt(4+x^2) = x-4
square both sides
4+x^2 = x^2-8x+16
You can finish.

Answer 2

4+√(4+x^2) = x
√(4+x^2) = x-4
square both sides
4+x^2 = x^2 - 8x + 16
8x = 12
x = 12/8 = 3/2

since we squared the equation, we MUST verify the answer
LS = 4 + √(4 + 9/4)
= 4 + √(25/4)
= 4 + 5/2
= 13/2

RS = 2/3
LS ≠ RS

so actually there is no solution.