Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Question:**
Which equation has the same solution as \( x^2 + 16x - 11 = 4 \)?
**Options:**
1. \( (x - 8)^2 = -49 \)
2. \( (x + 8)^2 = -49 \)
3. \( (x + 8)^2 = 79 \)
4. \( (x - 8)^2 = 79 \)
**Solution:**
In order to find which equation has the same solution as \( x^2 + 16x - 11 = 4 \), we first need to find the simplified form of the equation and compare it to the options provided:
1. Start by simplifying \( x^2 + 16x - 11 = 4 \):
\[ x^2 + 16x - 15 = 0 \]
2. To solve this, we complete the square:
- Move the constant term to the right side:
\[ x^2 + 16x = 15 \]
- Add and subtract \((\frac{16}{2})^2 = 64\) to complete the square:
\[ x^2 + 16x + 64 = 15 + 64 \]
\[ (x + 8)^2 = 79 \]
The correct equation that has the same solution is:
\[ (x + 8)^2 = 79 \]
Thus, the correct option is:
3. \( (x + 8)^2 = 79 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27baf55b-863d-43cd-b1bf-b876bb9f8c8b%2Fd2bd6c52-3726-4ed2-8847-d4adc1ca1462%2F3j3t7cy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Which equation has the same solution as \( x^2 + 16x - 11 = 4 \)?
**Options:**
1. \( (x - 8)^2 = -49 \)
2. \( (x + 8)^2 = -49 \)
3. \( (x + 8)^2 = 79 \)
4. \( (x - 8)^2 = 79 \)
**Solution:**
In order to find which equation has the same solution as \( x^2 + 16x - 11 = 4 \), we first need to find the simplified form of the equation and compare it to the options provided:
1. Start by simplifying \( x^2 + 16x - 11 = 4 \):
\[ x^2 + 16x - 15 = 0 \]
2. To solve this, we complete the square:
- Move the constant term to the right side:
\[ x^2 + 16x = 15 \]
- Add and subtract \((\frac{16}{2})^2 = 64\) to complete the square:
\[ x^2 + 16x + 64 = 15 + 64 \]
\[ (x + 8)^2 = 79 \]
The correct equation that has the same solution is:
\[ (x + 8)^2 = 79 \]
Thus, the correct option is:
3. \( (x + 8)^2 = 79 \)
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