To solve the equation √(x^2 - 8x + 16) + 2 = 7, we can start by isolating the square root term on one side of the equation.

Subtracting 2 from both sides, we get:

√(x^2 - 8x + 16) = 7 - 2

Simplifying, we have:

√(x^2 - 8x + 16) = 5

Next, we square both sides of the equation to eliminate the square root:

(x^2 - 8x + 16) = 5^2

Expanding and simplifying, we have:

x^2 - 8x + 16 = 25

Rearranging the equation, we get:

x^2 - 8x + 16 - 25 = 0

x^2 - 8x - 9 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -8, and c = -9. Plugging these values into the formula, we have:

x = (-(-8) ± √((-8)^2 - 4(1)(-9))) / (2(1))

Simplifying further:

x = (8 ± √(64 + 36)) / 2

x = (8 ± √100) / 2

x = (8 ± 10) / 2

Now, we have two possible solutions:

x = (8 + 10) / 2 = 18 / 2 = 9

x = (8 - 10) / 2 = -2 / 2 = -1

Therefore, the solutions to the equation √(x^2 - 8x + 16) + 2 = 7 are x = 9 and x = -1.