To solve the equation 6 - square root of x-2 = x + 4, you can follow these steps:
Start by isolating the square root term on one side of the equation. Subtract x + 4 from both sides to get:
6 - x - 4 - square root of x-2 = 0
Next, combine like terms:
2 - square root of x-2 = 0
Add square root of x-2 to both sides to get:
2 = square root of x-2
Now square both sides of the equation:
4 = x - 2
Finally, add 2 to both sides:
x = 6
So the solution is x = 6