(X+6)^2=16

To solve the equation \((X + 6)^2 = 16\), follow these steps:

1. Take the square root of both sides: \[ X + 6 = \pm 4 \]

2. This gives us two equations to solve: \[ X + 6 = 4 \quad \text{and} \quad X + 6 = -4 \]

3. Solve the first equation: \[ X + 6 = 4 \\ X = 4 - 6 \\ X = -2 \]

4. Solve the second equation: \[ X + 6 = -4 \\ X = -4 - 6 \\ X = -10 \]

So, the solutions to the equation \((X + 6)^2 = 16\) are: \[ X = -2 \quad \text{and} \quad X = -10 \]