Question
Solve the equation by factoring. What is/ are the correct solution(s)?
25x2−196=0
(1 point)
Responses
x=145
x is equal to 14 fifths
x=−145, x=145
x=−145, x=145
No solution
No solution
x=19625
25x2−196=0
(1 point)
Responses
x=145
x is equal to 14 fifths
x=−145, x=145
x=−145, x=145
No solution
No solution
x=19625
Answers
Answered by
GPT-4o mini
To solve the equation \(25x^2 - 196 = 0\) by factoring, we can start by rearranging the equation:
\[
25x^2 = 196
\]
Next, divide both sides by 25:
\[
x^2 = \frac{196}{25}
\]
Taking the square root of both sides gives us:
\[
x = \pm \sqrt{\frac{196}{25}} = \pm \frac{\sqrt{196}}{\sqrt{25}} = \pm \frac{14}{5}
\]
So, the solutions are:
\[
x = \frac{14}{5} \quad \text{and} \quad x = -\frac{14}{5}
\]
Thus, the correct response based on the solutions is:
**x=−145, x=145**
It appears the responses should have included the correct answered values as:
**x=−14/5, x=14/5**
However, based on the original options that were provided, the most accurate description of the solved roots in those particular choices would be missing. The best match to the simplified fractional expressions in standard form (if only formatted correctly) should have been added probably as an option for clarity.
\[
25x^2 = 196
\]
Next, divide both sides by 25:
\[
x^2 = \frac{196}{25}
\]
Taking the square root of both sides gives us:
\[
x = \pm \sqrt{\frac{196}{25}} = \pm \frac{\sqrt{196}}{\sqrt{25}} = \pm \frac{14}{5}
\]
So, the solutions are:
\[
x = \frac{14}{5} \quad \text{and} \quad x = -\frac{14}{5}
\]
Thus, the correct response based on the solutions is:
**x=−145, x=145**
It appears the responses should have included the correct answered values as:
**x=−14/5, x=14/5**
However, based on the original options that were provided, the most accurate description of the solved roots in those particular choices would be missing. The best match to the simplified fractional expressions in standard form (if only formatted correctly) should have been added probably as an option for clarity.