Question

What are the solutions of 4x2 - 16X = 16x - 39

Answer 1

x =
`(3)/(2)`, x =
`(13)/(2)`

Explanation:

Given

4x² - 16x = 16x - 39 ( subtract 16x - 39 from both sides )

4x² - 32x + 39 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term, that is

product = 4 × 39 = 156 and sum = - 32

The factors are - 26 and - 6

Use these factors to split the x- term

4x² - 26x - 6x + 39 = 0 ( factor the first/second and third/fourth terms )

2x(2x - 13) - 3(2x - 13) = 0 ← factor out (2x - 13) from each term

(2x - 13)(2x - 3) = 0

Equate each factor to zero and solve for x

2x - 3 = 0 ⇒ 2x = 3 ⇒ x =
`(3)/(2)`

2x - 13 = 0 ⇒ 2x = 13 ⇒ x =
`(13)/(2)`