Certainly! Let's solve the given equation step-by-step:
The given equation is:
[tex]\[ 15 + c^2 = 96 \][/tex]
1. Isolate \( c^2 \):
To isolate \( c^2 \), subtract 15 from both sides of the equation:
[tex]\[
15 + c^2 - 15 = 96 - 15
\][/tex]
Simplifying this, we get:
[tex]\[
c^2 = 81
\][/tex]
2. Solve for \( c \):
To find the value of \( c \), take the square root of both sides of the equation:
[tex]\[
c = \pm \sqrt{81}
\][/tex]
Since \( \sqrt{81} = 9 \), we have:
[tex]\[
c = \pm 9
\][/tex]
So, the solutions to the equation \( 15 + c^2 = 96 \) are \( c = 9 \) and \( c = -9 \), which are represented by:
[tex]\[
\varepsilon = \pm 9
\][/tex]
Thus, the correct answer is:
[tex]\[
\text{a. } \varepsilon = \pm 9
\][/tex]
