Answer:
PN = 70
Step-by-step explanation:
using the property that the diagonals bisect each other, then
PK = PN
5x = x² - 14 ( rearrange into standard form )
x² - 5x - 14 = 0 ← in standard form
(x - 7)(x + 2) = 0 ← in factored form
equate each factor to zero and solve for x
x - 7 = 0 ⇒ x = 7
x + 2 = 0 ⇒ x = - 2
but x > 0 ⇒ x = 7
PN = PK + KN = 5x + x² - 14 = (5 × 7) + 7² - 14 = 35 + 49 - 14 = 70
