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 Quadratic Equations: Example**
**Solve the equation. See Example 2.**
\[ 7x^2 - x = 0 \]
**Solution:**
To solve the equation, we can factor it:
\[
x(7x - 1) = 0
\]
Setting each factor equal to zero gives us:
1. \( x = 0 \)
2. \( 7x - 1 = 0 \)
Solving \( 7x - 1 = 0 \) yields:
\[
7x = 1
\]
\[
x = \frac{1}{7}
\]
Thus, the solutions to the equation are:
\[ x = 0 \] (smaller value) and \( x = \frac{1}{7} \) (larger value).
Substitute the values into the provided format:
\[ x = \boxed{0} \] (smaller value)
\[ x = \boxed{\frac{1}{7}} \] (larger value)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9896e9f0-21a4-41f5-9cfe-a9d2b9678883%2F0c8e2eea-4804-4878-811f-f55a60d9f6f7%2F4u2cuj_processed.png&w=3840&q=75)
Transcribed Image Text:**Solving Quadratic Equations: Example**
**Solve the equation. See Example 2.**
\[ 7x^2 - x = 0 \]
**Solution:**
To solve the equation, we can factor it:
\[
x(7x - 1) = 0
\]
Setting each factor equal to zero gives us:
1. \( x = 0 \)
2. \( 7x - 1 = 0 \)
Solving \( 7x - 1 = 0 \) yields:
\[
7x = 1
\]
\[
x = \frac{1}{7}
\]
Thus, the solutions to the equation are:
\[ x = 0 \] (smaller value) and \( x = \frac{1}{7} \) (larger value).
Substitute the values into the provided format:
\[ x = \boxed{0} \] (smaller value)
\[ x = \boxed{\frac{1}{7}} \] (larger value)
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