# Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x^2 + x – 4 =  0 - Mathematics

Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x2 + x – 4 =  0

#### Solution

2x2 + x – 4 = 0

⇒ 2x2 + x = 4

On dividing both sides of the equation, we get

⇒ x^2 + x/2 = 2

On adding (1/4)2 to both sides of the equation, we get

⇒ (x)^2 + 2 × x × 1/4 + (1/4)^2 = 2 + (1/4)^2

⇒ (x + 1/4)^2 = 33/16

⇒ x + 1/4 = ± sqrt33/4

⇒ x = ± sqrt33/4 - 1/4

⇒ x = ± sqrt33-1/4

⇒ x = (sqrt33-1)/4

Concept: Solutions of Quadratic Equations by Completing the Square
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#### APPEARS IN

NCERT Class 10 Maths
Exercise 4.3 | Q 1.2 | Page 87
RD Sharma Class 10 Maths