Final answer:
To solve the radical equation √(x+3) = x-3, square both sides of the equation and solve for x. The solutions are x = 1 and x = 6, but x = 1 is extraneous. Therefore, the valid solution is x = 6.
Step-by-step explanation:
To solve the radical equation √(x+3) = x-3, we can square both sides of the equation. This gives us x+3 = (x-3)^2. Expanding the right side, we get x+3 = x^2 - 6x + 9. Rearranging the equation to standard form, we have x^2 - 7x + 6 = 0.
Now, we can solve this quadratic equation by factoring or by using the quadratic formula. Factoring gives us (x-1)(x-6) = 0, so the solutions are x = 1 and x = 6.
However, we need to check our solutions to ensure they are valid. Plugging in x = 1, we get √(1+3) = 1-3, which simplifies to 2 = -2. This is not true, so x = 1 is extraneous. Plugging in x = 6, we get √(6+3) = 6-3, which simplifies to 3 = 3. This is true, so x = 6 is the valid solution.