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

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#### Solution

2x^{2} + x – 4 = 0

⇒ 2x^{2} + 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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