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

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=19625
x equals Start Fraction 196 over 25 End Fraction

x=−145, x=145

Answer 1

To solve the equation \(25x^2 - 196 = 0\) using the difference of squares pattern, we can first recognize that it can be factored as follows:

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

This can be expressed as a difference of squares:

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

Next, we set each factor equal to zero:

1. \(5x - 14 = 0\)
2. \(5x + 14 = 0\)

For the first equation:

\[5x - 14 = 0\]

Solving for \(x\):

\[5x = 14\] \[x = \frac{14}{5}\]

For the second equation:

\[5x + 14 = 0\]

Solving for \(x\):

\[5x = -14\] \[x = -\frac{14}{5}\]

Thus, the solutions are:

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

So the answer to the question is:

x=−145, x=145 (If we consider them in decimal form) as \(x\) values \(14/5\) and \(-14/5\). However, in decimal terms, it should be lined up correctly in responses provided.

It looks like the option that correctly represents the answers we found is not precisely matching any of the options provided. If we correct it to use the correct fractions, you should choose the one that represents x equals Start Fraction 14 over 5 End Fraction and x equals Start Fraction −14 over 5 End Fraction.