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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![**Solving \( x^2 + 4x + 5 = 0 \) by completing the square method**
To solve the quadratic equation \( x^2 + 4x + 5 = 0 \) by completing the square, we aim to express it in the form \( (x + h)^2 = k \).
1. Start with the given equation:
\[
x^2 + 4x + 5 = 0
\]
2. Move the constant term to the other side of the equation:
\[
x^2 + 4x = -5
\]
3. To complete the square, take half of the coefficient of \( x \), which is 4, divide by 2 to get 2, then square it to get 4:
\[
\left( \frac{4}{2} \right)^2 = 4
\]
4. Add this square term to both sides of the equation:
\[
x^2 + 4x + 4 = -5 + 4
\]
5. The left side is now a perfect square trinomial:
\[
(x + 2)^2 = -1
\]
Thus, comparing with the form \( (x + h)^2 = k \), we have \( h = 2 \) and \( k = -1 \).
**Find \( h \) and \( k \).**
\( h = \) [Enter your answer here]
\( k = \) [Enter your answer here]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f072395-e0a4-486f-9c92-023b53ab9ed9%2Fd11809d1-8253-495b-abb5-3ae29be279b7%2Fg6nuig_processed.png&w=3840&q=75)
Transcribed Image Text:**Solving \( x^2 + 4x + 5 = 0 \) by completing the square method**
To solve the quadratic equation \( x^2 + 4x + 5 = 0 \) by completing the square, we aim to express it in the form \( (x + h)^2 = k \).
1. Start with the given equation:
\[
x^2 + 4x + 5 = 0
\]
2. Move the constant term to the other side of the equation:
\[
x^2 + 4x = -5
\]
3. To complete the square, take half of the coefficient of \( x \), which is 4, divide by 2 to get 2, then square it to get 4:
\[
\left( \frac{4}{2} \right)^2 = 4
\]
4. Add this square term to both sides of the equation:
\[
x^2 + 4x + 4 = -5 + 4
\]
5. The left side is now a perfect square trinomial:
\[
(x + 2)^2 = -1
\]
Thus, comparing with the form \( (x + h)^2 = k \), we have \( h = 2 \) and \( k = -1 \).
**Find \( h \) and \( k \).**
\( h = \) [Enter your answer here]
\( k = \) [Enter your answer here]
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