Solve the following equation by factoring: 9x^2 – 3x – 2 = 0
2 answers:
Answer:
A
Step-by-step explanation:
Given
9x² - 3x - 2 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 9 × - 2 = - 18 and sum = - 3
The factors are - 6 and + 3
Use these factors to split the x- term
9x² - 6x + 3x - 2 = 0 ( factor the first/second and third/fourth terms )
3x(3x - 2) + 1(3x - 2) ← factor out (3x - 2) from each term
(3x - 2)(3x + 1) = 0
Equate each factor to zero and solve for x
3x - 2 = 0 ⇒ 3x = 2 ⇒ x =
3x + 1 = 0 ⇒ 3x = - 1 ⇒ x = -
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