Question

Factorise :- 4x^2-√3x-5 by completing the square.

Answer 1

Factorising 4x² - √3x - 5 by completing the square.

SOLUTION:

Here,

a = 4,

b = -√3,

and c = -5

4x² - √3x - 5 = 0

[Multiply 4a = 4(4) = 16 to both RHS and LHS]

16( 4x² - √3x - 5 = 0 ) = 16 × 0

⇒ 64x² -  16√3x - 80 = 0

[Take the constant to RHS]

⇒ 64x² -  16√3x = 80

[Try to put the LHS in the form (a+b)² or (a-b)² ]

⇒ (8x)² - 2 (8x) (√3) + (√3)² = (√3)² + 80

[ we take 8x = a, and √3 = b ]

⇒ (8x - √3)² = 3 + 80

[ (8x)² - 2 (8x) (√3) + (√3)² = (8x - √3)², in form (a)² - 2ab + (b)² = (a - b)² ]

⇒ (8x - √3)² = 83

⇒ 8x - √3 = ± √83

⇒ 8x = ± √83 + √3

⇒ x = $\boxed{\pm \frac{\sqrt{83}+\sqrt{3}}{8}}$