property of secants

Question

Find the value of x

Answer 1

According to secent rule 5(5+7) = x(x+4)

Distributive property a(b+c) = ab+ac

5(5)+5(7) = x(x)+x(4)                         

25+35 = x²+4x                     (Simplify)

x²+4x = 60

x²+4x-60 = 0

x²+10x-6x-60 = 0                (factors of left side)

x(x+10)-6(x+10) = 0

(x+10)(x-6) = 0

x+10 = 0 or x-6 = 0             (zero product property)

x = -10 or x = 6                 

The value of x is -10, 6.