Ginger was asked to solve 25x^2−196=0 by factoring using the Difference of Squares pattern. What is/are the correct solution(s)? (1 point) Responses A. x = −14/5, x = 14/5 b. x = 14/5 c. x = 196/25 D. There is no solution for x because the difference of squares pattern does not apply.
To solve the equation 25x^2−196=0 using the Difference of Squares pattern, we need to recognize that 25x^2 is the square of (5x), and 196 is the square of (14).
Therefore, the equation can be rewritten as (5x)^2 - 14^2 = 0.
Now we can factor using the Difference of Squares pattern, which states that (a^2 - b^2) can be factored as (a + b)(a - b).
Applying this pattern, the equation becomes (5x + 14)(5x - 14) = 0.
Setting each factor equal to zero, we get:
5x + 14 = 0
5x = -14
x = -14/5
Similarly,
5x - 14 = 0
5x = 14
x = 14/5
So the correct solutions are x = -14/5 and x = 14/5.
Therefore, the correct answer is A. x = −14/5, x = 14/5.