Ginger was asked to solve 25x^2−196=0
by factoring using the Difference of Squares pattern. What is/are the correct solution(s)?
To solve the equation 25x^2 - 196 = 0 by factoring using the Difference of Squares pattern, you need to rewrite it as the product of two perfect squares with opposite signs.
25x^2 - 196 can be factored as (5x)^2 - 14^2, which is a difference of squares.
Using the Difference of Squares pattern, the equation can be written as:
(5x - 14)(5x + 14) = 0
Setting each factor equal to 0, we can solve for x:
5x - 14 = 0 or 5x + 14 = 0
For the first equation, adding 14 to both sides gives:
5x = 14
Dividing both sides by 5 gives:
x = 14/5
For the second equation, subtracting 14 from both sides gives:
5x = -14
Dividing both sides by 5 gives:
x = -14/5
Therefore, the correct solutions are:
x = 14/5 and x = -14/5