Question

Solve for x. Write both solutions, separated by a
comma.
6x^2 + x-1=0

Answer 1

x = -
`(1)/(2)`, x =
`(1)/(3)`

Explanation:

Given

6x² + x - 1 = 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

product = 6 × - 1 = - 6 and sum = + 1

The factors are - 2 and + 3

Use these factors to split the x- term

6x² - 2x + 3x - 1 = 0 ( factor the first/second and third/fourth terms )

2x(3x - 1) + 1(3x - 1) = 0 ← factor out (3x - 1) from each term

(3x - 1)(2x + 1) = 0

Equate each factor to zero and solve for x

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = -
`(1)/(2)`

3x - 1 = 0 ⇒ 3x = 1 ⇒ x =
`(1)/(3)`