Problem: (x-16)^2 + (x-2)^2=x^2
(x - 16)^2 + (x - 2)^2 = x^2
(x - 16)^2 + (x - 2)^2 - (x - 2)^2 = x^2 - (x - 2)^2
(x - 16)^2 = x^2 - (x - 2)^2 ... square of side a = square of hypotenuse - square of side b
x^2 - 32x + 256 = x^2 - (x^2 - 4x + 4)
x^2 - 32x + 256 = 4x - 4
x^2 - 32x + 256 - 4x + 4 = 4x - 4 - 4x + 4
x^2 - 32x + 256 - 4x + 4 = 0
x^2 - 36x + 260 = 0
(x - 26)(x - 10) = 0
Set each factor to zero and solve for x.
x - 26 = 0
x = 26
x - 10 = 0
x = 10
Check.
(x - 16)^2 + (x - 2)^2 = x^2
(26 - 16)^2 + (26 - 2)^2 = 26^2
10^2 + 24^2 = 26^2
100 + 576 = 676
676 = 676
(x - 16)^2 + (x - 2)^2 = x^2
(10 - 16)^2 + (10 - 2)^2 = 10^2
-6^2 + 8^2 = 10^2
36 + 64 = 100
100 = 100
Answer: x = 26 and x = 10