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)

Question

Responses

x=145
x equals Start Fraction 14 over 5 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=145
x equals negative Start Fraction 14 over 5 End Fraction , x equals Start Fraction 14 over 5 End Fraction

x=19625

Answer 1

To solve the equation \(25x^2 - 196 = 0\) using the difference of squares pattern, we can rewrite it as:

\[ 25x^2 - 196 = (5x)^2 - (14)^2 = 0 \]

Now we can apply the difference of squares formula \(a^2 - b^2 = (a - b)(a + b)\):

\[ (5x - 14)(5x + 14) = 0 \]

Setting each factor equal to zero gives us the solutions:

1. \(5x - 14 = 0\) \[ 5x = 14 \implies x = \frac{14}{5} \]

2. \(5x + 14 = 0\) \[ 5x = -14 \implies x = -\frac{14}{5} \]

Thus, the solutions are:

\[ x = \frac{14}{5} \quad \text{and} \quad x = -\frac{14}{5} \]

In summary, the correct responses are:

• \(x = -\frac{14}{5}, x = \frac{14}{5}\)