Solve the equation by factoring. What is/ are the correct solution(s)?

Question

25x^2−196=0
(1 point)
Responses

x= 14/5
x is equal to 14 fifths

x= 196/25
x is equal to 196 over 25

No solution
No solution

x=−14/5, x=14/5

Answer 1

To solve the equation \( 25x^2 - 196 = 0 \) by factoring, we can rewrite it as follows:

1. Rearrange the equation: \( 25x^2 = 196 \)
2. Divide both sides by 25: \( x^2 = \frac{196}{25} \)
3. Take the square root of both sides:

\[ x = \pm \sqrt{\frac{196}{25}} = \pm \frac{\sqrt{196}}{\sqrt{25}} = \pm \frac{14}{5} \]

Thus, the solutions are \( x = \frac{14}{5} \) and \( x = -\frac{14}{5} \).

Therefore, the correct answer is:

x = −14/5, x = 14/5