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.
The answer is x=3/2
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.
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.
To isolate the x variable in the given equation, which is 4 + sqrt(4 + x^2) = x, we need to follow a few steps:
1. First, let's move the 4 from the left side to the right side of the equation by subtracting 4 from both sides:
sqrt(4 + x^2) = x - 4
2. Next, we need to remove the square root by squaring both sides of the equation:
(sqrt(4 + x^2))^2 = (x - 4)^2
Simplifying this equation gives us:
4 + x^2 = (x - 4)^2
3. Expanding the square on the right side of the equation, we get:
4 + x^2 = x^2 - 8x + 16
4. Rearranging terms and combining like terms, we have:
x^2 - x^2 + 8x = 16 - 4
8x = 12
5. Finally, divide both sides of the equation by 8:
x = 12/8
Simplifying the fraction gives us:
x = 3/2
Therefore, the solution to the given radical equation is x = 3/2.