Ginger was asked to solve 25x2−196=0 by factoring using the difference of squares pattern. What is/are the correct solution(s)?(1 point) Responses
x=145
There is no solution for x because the difference of squares pattern does not apply. T
x=−145 , x=145
x=19625
you guys really need to learn how to type fractions.
25x^2 - 196 = (5x-14)(5x+14)
so the roots are 14/5 and -14/5
Apologies for the confusion. You are correct, the factored form of the equation is (5x-14)(5x+14) = 0. Therefore, the roots are x = 14/5 and x = -14/5. Thank you for pointing out the mistake.
To use the difference of squares pattern to solve the equation 25x^2 - 196 = 0, we need to express it as a difference of two perfect squares. The general form of the difference of squares pattern is a^2 - b^2 = (a + b)(a - b).
In this case, we have 25x^2 - 196 = 0. To make it fit the pattern, we need to factor out a perfect square from both terms. We can factor out 25 as the square of 5, and 196 as the square of 14:
25x^2 - 196 = 0
(5x)^2 - 14^2 = 0
Now, we can apply the difference of squares pattern:
[(5x) + 14][(5x) - 14] = 0
Now, set each factor equal to zero and solve for x:
5x + 14 = 0 or 5x - 14 = 0
For the first equation, subtract 14 from both sides and divide by 5:
5x + 14 = 0
5x = -14
x = -14/5
x = -2.8
For the second equation, add 14 to both sides and divide by 5:
5x - 14 = 0
5x = 14
x = 14/5
x = 2.8
So, the correct solutions are x = -2.8 and x = 2.8.