Answer :

12 units

Step-by-step explanation :

Given quadratic equation,

 2x² + x - 300 = 0

It is of the form ax² + bx + c = 0

we KNOW,

quadratic term = ax²

linear term = bx

constant term = c

Hence for the given quadratic equation,

Quadratic term = 2x²

Linear term = x

Constant term = -300

Steps to factorize :

>> Find the product of quadratic term[ax²] and constant term[bx]

     = 2x² × (-300)

     = -600x²

>> Find the factors of ''-600x²'' in pairs,

     (x) (-600x)

     (-x) (600x)

    (2x) (-300x)

    (-2x) (300x)

    (3x) (-200x)  

    (-3x) (200x)

    (4x) (-150x)

    (-4x) (150x)

    (5x) (-120x)  

    (-5x) (120x)

    (6x) (-100X)  

    (-6x) (100x)

    (8x) (-75x)  

    (-8x) (75x)

    (10x) (-60x)  

    (-10x) (60x)

    (12x) (-50X)  

    (-12x) (50x)

    (15x) (-40x)

    (-15x) (40x)

    (24x) (-25x)

    (-24x) (25x)

    (30x) (-20x)

    (-30x) (20x)

>>  From the above, find the PAIR that adds to get linear term[bx]

    25x - 24x = x

>> SPLIT x as 25x and -24x

   2x² + x - 300 = 0

   2x² - 24x + 25x - 300 = 0

>> Find the common factor

   2x(x - 12) + 25(x - 12) = 0

     (x - 12) (2x + 25) = 0

=> x - 12 = 0 ; x = 12

=> 2x + 25 = 0 ; x = -25/12

The dimensions of the room can't be negative.

Hence, x = 12

Therefore, the length and breadth of the room = 12 units