Answer:
x = 5
Step-by-step explanation:
Two secants have equal ratios when (in this case) they are split up as
AB * AC = AD*AE
Givens
AB = x-2
AC = (x - 2 + x+ 4) = 2x + 2
AD = 4
AE = 5 + 4 = 9
Substitute and solution
(x - 2) (2x + 2) = 4 (9) Expand the left, Combine the right
2(x^2 - x - 2) = 36 Divide both sides by 2
x^2 - x - 2 = 18 Subtract 18 from both sides
x^2 - x - 2 - 18 = 18 - 18 Combine
x^2 - x - 20 = 0 This factors
(x - 5)(x + 4) = 0 Only one of these factors works
x - 5 = 0 Add 5 to both sides.
x = 5
