Answer:
CE = 35
Step-by-step explanation:
BD is parallel to AE and intersects the other 2 sides, dividing those sides proportionally, that is
[tex]\frac{14}{2x+3}[/tex] = [tex]\frac{x-5}{6}[/tex] ( cross- multiply )
(x - 5)(2x + 3) = 84 ← expand left side using FOIL
2x² - 7x - 15 = 84 ( subtract 84 from both sides )
2x² - 7x - 99 = 0 ← in standard form
(2x + 11)(x - 9) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 9 = 0 ⇒ x = 9
2x + 11 = 0 ⇒ 2x = - 11 ⇒ x = - [tex]\frac{11}{2}[/tex]
but x > 0 , thus x = 9
Then
CE = 14 + 2x + 3
= 17 + 2(9)
= 17 + 18
= 35
