Find the roots of the quadratic equation x² + 4x – 5 = 0 by the method of completing the square.

Given quadratic equation is: x² + 4x – 5 = 0

Comparing the equation with the standard form, we get: 

b = 4, c = -5

⇒ (x + $\frac{\mathrm{b}}{2}$)² = - (c – $\frac{{\mathrm{b}}^2}{4}$)

So, [x + ($\frac{4}{2}$)]² = - [- 5 – ($\frac{4^2}{4}$)]

⇒ (x + 2)² = 5 + 4

⇒ (x + 2)² = 9

⇒ (x + 2) = ±√9

⇒ (x + 2) = ± 3

⇒ x + 2 = 3, x + 2 = -3

⇒ x = 1 , -5

Therefore, the roots of the given equation are 1 and -5.