Use completing the square method to solve: x² + 4x – 21 = 0.

Given equation: x² + 4x – 21 = 0.

By comparing the general quadratic equation. i.e. ax² + bx + c = 0.

We have, a = 1, b = 4 and c = –21.

m = $\frac{\mathrm{b}}{2\mathrm{a}} =\frac{4}{2} = 2$

n = $\mathrm{c} - \frac{{\mathrm{b}}^2}{4\mathrm{a}} = - 21 - \frac{16}{4}= -21 - 4 = - 25$

So, the equation is solved as: a(x + m)² + n

=> (x + 2)² – 25 = 0

=> (x + 2)² - (5)² = 0 

=> x + 2 = ±5

=> x = 3, –7

So, the roots are 3, - 7.