a² ± 2ab + b² = (a + b)²
a² = b²  ----> a² - b² = (a - b)(a + b)
~~~~~~~~~~~
x² - 16x + 64 = 49 ---->  (x - 8)² - 49 = 0
(x - 8)² - 7² = 0 ----> (x - 8 - 7)(x - 8 + 7) = 0 ---> (x - 15)(x - 1) = 0
x = 15 or x = 1

To solve using the square root method, the first step is to make the left side into a squared term.

We're looking for something of the format (x - #)^2, we need the negative because the middle term is negative.

So we have (x - #)^2 = x^2 - 16x + 64,

Take the square root of 64 and you get 8.

So we have (x - 8)^2, which is equal to 49 (from the original problem)

Now we can use the square root property

(x-8)^2 = 49

(x-8) = + or - the square root of 49

x - 8 = + or - 7

x = 7 + 8 = 15  AND x = -7 + 8 = 1

So you get x = 1, 15

Hope this helps you, Sarah! Feel free to message me if you have any other questions :)

Katherine

First, start by looking at the problem: x^2 - 16x + 64 = 49

You can subtract 49 from both sides to simplify the problem. You are left with: x^2 - 16x + 15 = 0

Now try to reverse foil  x^2 - 16x + 15.

Think what adds to get 16, but multiplied = 15?

15 x 1 = 15 and 15+ 1 = 16

Because the 16 is negative in this problem, both the 15 and 1 would have to be negative.  So:

(x - 15) and (x - 1) would equal x^2 - 16x + 15 with the foil method. Since x - 15 would have to mean x = 15 and because x - 1 would have to mean x = 1,  plug  15 and 1 into the original problem, to recheck that these factors are correct:

(15)^2 - 16(15) + 64 = 49

225 - 240 + 64 = 49

Now lets try (x - 1):
(1)^2 - 16(1) + 64 = 49

1 - 16 + 64 = 49

So (x - 1) and (x - 15) are both factors of x^2 - 16x + 64 = 49

So x = 15 or x = 1