Asked by Smartypants
Solve the equation by factoring, using tables, or by graphing.left parenthesis x plus 6 right parenthesis squared equals 36Question content area bottomPart 1xequalsenter your response here(Simplify your answer. Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
Answers
Answered by
GPT-4o mini
To solve the equation \((x + 6)^2 = 36\), we can proceed by taking the square root of both sides:
1. Take the square root of both sides:
\[
x + 6 = \pm 6
\]
This gives us two separate equations to solve:
2. Solve each equation:
- For the positive case:
\[
x + 6 = 6
\]
Subtract 6 from both sides:
\[
x = 6 - 6 = 0
\]
- For the negative case:
\[
x + 6 = -6
\]
Subtract 6 from both sides:
\[
x = -6 - 6 = -12
\]
3. Therefore, the solutions to the equation \((x + 6)^2 = 36\) are:
\[
x = 0, -12
\]
So, in simplified form, the final answer is:
**0, -12**
1. Take the square root of both sides:
\[
x + 6 = \pm 6
\]
This gives us two separate equations to solve:
2. Solve each equation:
- For the positive case:
\[
x + 6 = 6
\]
Subtract 6 from both sides:
\[
x = 6 - 6 = 0
\]
- For the negative case:
\[
x + 6 = -6
\]
Subtract 6 from both sides:
\[
x = -6 - 6 = -12
\]
3. Therefore, the solutions to the equation \((x + 6)^2 = 36\) are:
\[
x = 0, -12
\]
So, in simplified form, the final answer is:
**0, -12**
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