To solve the given equation [tex]\(25m^2 = 196\)[/tex], we will follow a step-by-step approach.
1. Isolate [tex]\(m^2\)[/tex]:
Start by dividing both sides of the equation by 25 to isolate [tex]\(m^2\)[/tex]:
[tex]\[
\frac{25m^2}{25} = \frac{196}{25}
\][/tex]
This simplifies to:
[tex]\[
m^2 = \frac{196}{25}
\][/tex]
2. Calculate the value of [tex]\(\frac{196}{25}\)[/tex]:
The result of the division is:
[tex]\[
m^2 = 7.84
\][/tex]
3. Solve for [tex]\(m\)[/tex]:
To find [tex]\(m\)[/tex], we need to take the square root of both sides of the equation. Remember, taking the square root of a number can yield both positive and negative results:
[tex]\[
m = \pm \sqrt{7.84}
\][/tex]
4. Determine the square roots:
The positive square root of 7.84 is:
[tex]\[
\sqrt{7.84} = 2.8
\][/tex]
The negative square root of 7.84 is:
[tex]\[
-\sqrt{7.84} = -2.8
\][/tex]
So, the solutions for [tex]\(m\)[/tex] are:
[tex]\[
m = 2.8, -2.8
\][/tex]
Therefore, the answers, in comma-separated form, are:
[tex]\[
2.8, -2.8
\][/tex]
