Answer:
x = 12
Step-by-step explanation:
x^2 + (x - 7)^2 = (x + 1)^2
x^2 + x^2 - 14x + 49 = x^2 + 2x + 1
x^2 - 16x + 48 = 0
(x - 4)(x - 12) = 0
x - 4 = 0 or x - 12 = 0
x = 4 or x = 12
One side has length x - 7.
For x = 4, x - 7 = 4 - 7 = -3.
Since a side of a triangle cannot have a negative length, x = 4 must be discarded.
Answer: x = 12
