Question

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

2x² + x – 4 = 0

Answer 1

Given: 2x² + x – 4 = 0

⇒ 2x² + x = 4 

⇒ (√2x)² + x = 4 

⇒ (√2x)² + 2.√2.x. \(\frac{1}{2\sqrt{2}}\)= 4 

Now LHS is in the form a² + 2ab

where b = \(\frac{1}{2\sqrt{2}}\)

Adding b² = \((\frac{1}{2\sqrt{2}})^2\) on both sides we get