property of secants

Question

Find value of x

Answer 1

According to tangent rule 6×6 = x (x +5)

x (x +5) = 36

x²+5x = 36

x²+5x-36 = 0                   (factor of left side)

x²+9x-4x-36 = 0

x(x+9)-4(x+9) = 0

(x+9)(x-4) = 0

x+9 = 0 or x-4 = 0            (zero product property)

x = -9 or x = 4

Solution: x = -9 or x = 4.