Answer: x = ⁵/₃; x = 5
Step-by-step explanation:
Since (20) = (-3) [we can cross multiply]
(x²- 25) (5-x)
⇒ (20)(5 - x) = (-3)(x² - 25) [expand the brackets]
⇒ 100 - 20x = -3x² + 75 [make the equation equal to zero]
⇒ 3x² - 20x + 25 = 0 [expand the middle term using
appropriate factors of the product
of the terms a and c (3 × 25)]
⇒ 3x² - 15x - 5x + 25 = 0 [factorize the terms]
⇒ (3x - 5 ) (x - 5) = 0 [using the knowledge that for the
produc to be 0, one of terms
must be zero]
⇒ (3x - 5 ) = 0 OR (x - 5) = 0 [solve for x in each case]
⇒ x = ⁵/₃ OR x = 5
