Find the roots of the following quadratic equations, if they exist, by the method of completing the square:

2x^2 + x – 4 = 0

Dear Student

⇒ 2x^2 + x = 4
Dividing both sides of the equation by 2,
⇒ x^2 +x/2 = 2
Now on adding (1/4)^2 to both sides of the equation,
⇒ (x)^2 + 2 × x × 1/4 + (1/4)^2 = 2 + (1/4)^2
⇒ (x + 1/4)^2 = 33/16
⇒ x + 1/4 = ± √33/4
⇒ x = ± √33/4 - 1/4
⇒ x = ± √33-1/4
either
x = √33-1/4 or x = -√33-1/4

Thanks