Answer:
x = 5, x = 7
Step-by-step explanation:
Tangents to a circle from an external point are congruent, that is
x² = 12x - 35 ( subtract 12x - 35 from both sides )
x² - 12x + 35 = 0 ← in standard form
Consider the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (- 12)
The factors are - 5 and - 7, since
- 5 × - 7 = + 35 and - 5 - 7 = - 12, thus
(x - 5)(x - 7) = 0
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x - 7 = 0 ⇒ x = 7
smallest value of x is 5
largest value of x is 7
