Question

Use the work shown to find the solutions of the quadratic equation. x2 – x –3/4=0 x2 – x = 3/4

Answer 1

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

Explanation:

Given

x² - x -
`(3)/(4)` = 0

Multiply through by 4 to clear the fraction

4x² - 4x - 3 = 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 × - 3 = - 12 and sum = - 4

The factors are + 2 and - 6

Use these factors to split the x- term

4x² + 2x - 6x - 3 = 0 ( factor the first/second and third/fourth terms )

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

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

Equate each factor to zero and solve for x

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

2x - 3 = 0 ⇒ 2x = 3 ⇒ x =
`(3)/(2)`