Ginger was asked to solve 25x^2−196=0

Question

 by factoring using the difference

Answer 1

of squares.

To solve this equation, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, we have 25x^2 - 196, which can be rewritten as (5x)^2 - 14^2.

Using the difference of squares formula, we can factor it as:

(5x + 14)(5x - 14) = 0.

Set each factor equal to zero and solve for x:

5x + 14 = 0 ; 5x - 14 = 0.

Solving these equations, we get:

5x = -14 ; 5x = 14.

Dividing both sides by 5, we find:

x = -14/5 ; x = 14/5.

Therefore, the solutions to the equation 25x^2 - 196 = 0 are x = -14/5 and x = 14/5.