Question

Solve the following quadratic equation by completing the square method.

x² + 2x – 5 = 0

Answer 1

x² + 2x – 5 = 0 

Comparing x² + 2x with x² + 2xy,

2xy = 2x

∴ y = 1

∴ y² = 1

∴ x² + 2x + 1 is a perfect square trinomial.

x² + 2x – 5 = 0 

∴ x² + 2x + 1 − 1 − 5 = 0

∴ (x + 1)² − 6 = 0

∴ `(x + 1)^2 - (sqrt 6)^2` = 0

∴ `(x + 1 + sqrt 6) (x + 1 - sqrt 6)` = 0

∴ `x + 1 + sqrt 6` = 0 or `x + 1 - sqrt 6` = 0

∴ x = `-1 - sqrt 6` or x = `-1 + sqrt 6`

`-1 - sqrt 6, -1 + sqrt 6` are the roots of the given quadratic equation.