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=19625 x equals Start Fraction 196 over 25 End Fraction There is no solution for x because the difference of squares pattern does not apply. There is no solution for x because the difference of squares pattern does not apply. x=145 x equals Start Fraction 14 over 5 End Fraction x=−145 , x=145
To solve 25x^2 - 196 = 0 by factoring using the difference of squares pattern, we can rewrite the equation as:
(5x)^2 - 14^2 = 0
This expression can be factored as a difference of squares:
(5x - 14)(5x + 14) = 0
Setting each factor equal to zero:
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
To solve the equation 25x^2 - 196 = 0 using the difference of squares pattern, we need to rewrite the equation in the form of (a^2 - b^2) = 0.
First, let's rewrite the equation as a perfect square minus another perfect square: (5x)^2 - (14)^2 = 0.
Now, we can rewrite the equation as (5x + 14)(5x - 14) = 0.
To find the solutions, set each factor equal to zero and solve for x:
1) 5x + 14 = 0
5x = -14
x = -14/5 (simplified form: x = -2.8)
2) 5x - 14 = 0
5x = 14
x = 14/5 (simplified form: x = 2.8)
So, the correct solutions are x = -2.8 and x = 2.8.
To solve the equation 25x^2 - 196 = 0 using the difference of squares pattern, we need to factor the equation.
First, let's write it as a difference of squares:
(5x)^2 - 14^2 = 0
Now, we can use the formula for the difference of squares:
(a^2 - b^2) = (a + b)(a - b)
So, in our case, the equation can be factored as:
(5x + 14)(5x - 14) = 0
To find the correct solution(s), we set each factor equal to zero and solve for x:
5x + 14 = 0 → 5x = -14 → x = -14/5 (or x = -2.8)
5x - 14 = 0 → 5x = 14 → x = 14/5 (or x = 2.8)
Therefore, the correct solution(s) are:
x = -14/5 and x = 14/5