The value of length CE is 35.BD is parallel to AE and intersects the other 2 sides, dividing those sides proportionally, that is(x - 5)(2x + 3) = 84 ← expand left side using FOIL2x² - 7x - 15 = 84 ( subtract 84 from both sides )2x² - 7x - 99 = 0 ← in standard form(2x + 11)(x - 9) = 0 ← in factored formEquate each factor to zero and solve for xx - 9 = 0 ⇒ x = 92x + 11 = 0 ⇒ 2x = - 11 ⇒ x = -but x > 0 , thus x = 9ThenCE = 14 + 2x + 3CE = 17 + 2(9)CE = 17 + 18CE= 35Therefore, The value of length CE is 35...

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