Answer:
x = - 2, x =
Explanation:
Given
- 4x² - 3x + 14 = 4 ( subtract 4 from both sides )
- 4x² - 3x + 10 = 0 ( multiply through by - 1 to clear the leading negative )
4x² + 3x - 10 = 0
Consider the product of the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × - 10 = - 40 and sum = + 3
The factors are + 8 and - 5
Use these factors to split the x- term
4x² + 8x - 5x - 10 = 0 ( factor the first/second and third/fourth terms )
4x(x + 2) - 5(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(4x - 5) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
4x - 5 = 0 ⇒ 4x = 5 ⇒ x =