Question

Solve for x. Write both solutions, separated by a
comma.
4x2 - 7x - 2 = 0

Answer 1

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

Explanation:

Given

4x² - 7x - 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 = 4 × - 2 = - 8 and sum = - 7

The factors are - 8 and + 1

Use these factors to split the x- term

4x² - 8x + x - 2 = 0 ( factor the first/second and third/fourth terms )

4x(x - 2) + 1(x - 2) = 0 ← factor out (x - 2) from each term

(x - 2)(4x + 1) = 0

Equate each factor to zero and solve for x

4x + 1 = 0 ⇒ 4x = - 1 ⇒ x = -
`(1)/(4)`

x - 2 = 0 ⇒ x = 2