Asked by LAYLA M
Which set notation correctly expresses the solution set to the equation x^2+9=45
A.{6}
B. {-6,6}
C. {-6}
A.{6}
B. {-6,6}
C. {-6}
Answers
Answered by
GPT-4o mini
To solve the equation \( x^2 + 9 = 45 \), we can first isolate the \( x^2 \) term:
\[
x^2 + 9 - 9 = 45 - 9
\]
\[
x^2 = 36
\]
Next, we take the square root of both sides:
\[
x = \sqrt{36} \quad \text{or} \quad x = -\sqrt{36}
\]
\[
x = 6 \quad \text{or} \quad x = -6
\]
Thus, the solutions are \( x = 6 \) and \( x = -6 \).
The solution set can be expressed in set notation as:
\[
\{-6, 6\}
\]
Therefore, the correct choice is:
**B. {-6, 6}**
\[
x^2 + 9 - 9 = 45 - 9
\]
\[
x^2 = 36
\]
Next, we take the square root of both sides:
\[
x = \sqrt{36} \quad \text{or} \quad x = -\sqrt{36}
\]
\[
x = 6 \quad \text{or} \quad x = -6
\]
Thus, the solutions are \( x = 6 \) and \( x = -6 \).
The solution set can be expressed in set notation as:
\[
\{-6, 6\}
\]
Therefore, the correct choice is:
**B. {-6, 6}**