Solution of x2 – x – StartFraction 3 Over 4 EndFraction = 0?

x = - , x =

Step-by-step explanation:

Given

x² - x - = 0

Multiply through by 4 to clear the fraction

4x² - 4x - 3 = 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 = 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) ← 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 = -

2x - 3 = 0 ⇒ 2x = 3 ⇒ x =