Question

solve for k.
$k^2 + 15 = 31$
write your answers as integers or as proper or improper fractions in simplest form.
k = \boxed{} or k = \boxed{}

Explanation:

Step1: Subtract 15 from both sides

To isolate \(k^2\), we subtract 15 from both sides of the equation \(k^2 + 15 = 31\).
\[
k^2 + 15 - 15 = 31 - 15
\]
Simplifying both sides gives:
\[
k^2 = 16
\]

Step2: Take square root of both sides

To solve for \(k\), we take the square root of both sides. Remember that when we take the square root of a number, we get both a positive and a negative solution.
\[
k = \pm\sqrt{16}
\]
Since \(\sqrt{16} = 4\), we have:
\[
k = 4 \text{ or } k = -4
\]

Answer:

\(k = 4\) or \(k = -4\)