Question

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

. 2x^2-7x+3=0

Answer 1

2x^2 – 7x + 3 = 0

⇒ 2x^2 – 7x = - 3

On dividing both sides of the equation by 2, we get

⇒ x^2 – 7x/2 = -3/2

⇒x^2 – (2 × x × 7/4) = -3/2

On adding (7/4)^2 to both sides of equation, we get

⇒ (x)^2 - 2 × x × 7/4 + (7/4)^2 = (7/4)^2 - 3/2


⇒ (x - 7/4)^2 = 49/16 - 3/2

⇒ (x - 7/4)^2 = 25/16

⇒ (x - 7/4) = ± 5/4

⇒ x = 7/4 ± 5/4

⇒ x = 7/4 + 5/4
or
x = 7/4 - 5/4

⇒ x = 12/4 or x = 2/4

⇒ x = 3 or 1/2