Question

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

Answer 1

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

Answer 2

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