Expand the expression in the equation
$$\left(x + 5\right)^{2} = 0$$
We get the quadratic equation
$$x^{2} + 10 x + 25 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 10$$
$$c = 25$$
, then
D = b^2 - 4 * a * c =
(10)^2 - 4 * (1) * (25) = 0
Because D = 0, then the equation has one root.
x = -b/2a = -10/2/(1)
$$x_{1} = -5$$