Find the value of x.

x = 5

Step-by-step explanation:

Given 2 secants from an external point to the circle, then

the product of the external part and the entire secant of one is equal to the product of the external part and the entire secant of the other, that is

(x - 2)(x - 2 + x + 4) = 4(4 + 5)

(x - 2)(2x + 2) = 4 × 9

2x² + 2x - 4x - 4 = 36 ( subtract 36 from both sides )

2x² - 2x - 40 = 0 ( divide through by 2 )

x² - x - 20 = 0 ← in standard form

(x - 5)(x + 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 4 = 0 ⇒ x = - 4

But x > 0 , then x = 5