X^2 - 25 = 0. Factor and use the zero product property to solve.

X^2 - 25 is a difference of squares which has a special factorization.

In general, a^2 - b^2 = (a + b) (a - b)

x^2 - 25 = 0

(x + 5) (x - 5) = 0

x + 5 = 0 or x - 5 = 0

x = - 5 or x = 5

Ax^2 + bx + c = 0

a = 1, b = 0, c = - 25

Quadratic formula:

x = {-b + / - sqrt (b^2 - 4ac) } / 2a

x = {0 + / - sqrt (0 - 4 (1) (-25)) } / 2 (1)

x = + / - sqrt (100) / 2

x = + / - 10/2

x = + / - 5

Factored: (x - 5) (x + 5)

Solutions: 5 and - 5