Question

2x^2-x-360=0 split this equation ​

Answer 1

2x² - x - 360 = 0

Coefficient of x = -1.

Let -1 = a + b such that ab = 2 · (-360) = -720.

Let a = u + v and b = u - v.

a + b = -1

=> u + v + u - v = -1

=> 2u = -1

=> u = -1/2

=> u² = 1/4

ab = -720

=> (u + v)(u - v) = -720

=> u² - v² = -720

=> 1/4 - v² = -720

=> v² = 720 + 1/4

=> v² = 2881/4

=> v = √2881/2

a = u + v = (√2881 - 1)/2

b = u - v = - (√2881 + 1)/2

Hence, the middle term should be split as,

- x = [(√2881 - 1)/2]x - [(√2881 + 1)/2]x

So,

2x² - x - 360 = 0

=> 2x² + [(√2881 - 1)/2]x - [(√2881 + 1)/2]x - 360 = 0

=> x[2x + (√2881 - 1)/2] - [(√2881 + 1)/4][2x + (√2881 - 1)/2]

=> [2x + (√2881 - 1)/2] [x - (√2881 + 1)/4]

Hence Factorised!