Ginger was asked to solve 25x2−196=0%0D%0A25%0D%0A%0D%0A2%0D%0A−%0D%0A196%0D%0A=%0D%0A0%0D%0A by factoring using the difference of squares pattern. What is/are the correct solution(s)?
To solve the equation 25x^2 - 196 = 0, we can use the difference of squares pattern. The difference of squares pattern states that for any equation of the form a^2 - b^2 = 0, it can be factored as (a + b)(a - b) = 0.
In this case, a^2 is 25x^2 and b^2 is 196. Taking the square root of both sides, we have:
a + b = sqrt(25x^2) + sqrt(196) = 5x + 14
a - b = sqrt(25x^2) - sqrt(196) = 5x - 14
Therefore, factoring the equation using the difference of squares pattern yields:
(5x + 14)(5x - 14) = 0
Setting each factor equal to zero and solving for x:
5x + 14 = 0
5x = -14
x = -14/5
5x - 14 = 0
5x = 14
x = 14/5
Therefore, the correct solutions are x = -14/5 and x = 14/5.