.com/alekscgi/x/Isl.exe/1o_u-IgNsikr7j8P3jH-IJIMpwvejtT6KR WCS Bookmarks New Tab Williamson Schools O QUADRATIC FUNCTIONS AND EQUATIONS Applying the quadratic formula: Exact answers Use the quadratic formula to solve for x. 2x-6x-1=0 (If there is more than one solution, separate them with commas.)
.com/alekscgi/x/Isl.exe/1o_u-IgNsikr7j8P3jH-IJIMpwvejtT6KR WCS Bookmarks New Tab Williamson Schools O QUADRATIC FUNCTIONS AND EQUATIONS Applying the quadratic formula: Exact answers Use the quadratic formula to solve for x. 2x-6x-1=0 (If there is more than one solution, separate them with commas.)
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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![### Quadratic Functions and Equations
#### Applying the Quadratic Formula: Exact Answers
**Problem Statement:**
Use the quadratic formula to solve for \( x \).
\[ 2x^2 - 6x - 1 = 0 \]
*(If there is more than one solution, separate them with commas.)*
**Answer Box:**
\[ x = \quad \]
---
### Explanation:
To solve the quadratic equation \( 2x^2 - 6x - 1 = 0 \) using the quadratic formula, follow these steps:
1. Identify the coefficients \( a \), \( b \), and \( c \) from the equation \( ax^2 + bx + c = 0 \).
- Here, \( a = 2 \), \( b = -6 \), and \( c = -1 \).
2. Substitute the coefficients into the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
3. Calculate the discriminant \( b^2 - 4ac \):
\[ (-6)^2 - 4(2)(-1) = 36 + 8 = 44 \]
4. Substitute the discriminant back into the quadratic formula:
\[ x = \frac{6 \pm \sqrt{44}}{4} \]
5. Simplify the expression:
\[ x = \frac{6 \pm 2\sqrt{11}}{4} = \frac{3 \pm \sqrt{11}}{2} \]
6. Write down the solutions:
\[ x = \frac{3 + \sqrt{11}}{2}, \frac{3 - \sqrt{11}}{2} \]
Thus, the solutions to the equation are:
\[ x = \frac{3 + \sqrt{11}}{2}, \frac{3 - \sqrt{11}}{2} \]
### Instructions:
Enter the solutions in the provided answer box, separating them with commas if there is more than one solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc3f58a8-8dfb-4cee-aa0a-39cd0da35c96%2F00b35402-6484-432b-a03d-5f51b17f3f82%2Fq6d5exq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Quadratic Functions and Equations
#### Applying the Quadratic Formula: Exact Answers
**Problem Statement:**
Use the quadratic formula to solve for \( x \).
\[ 2x^2 - 6x - 1 = 0 \]
*(If there is more than one solution, separate them with commas.)*
**Answer Box:**
\[ x = \quad \]
---
### Explanation:
To solve the quadratic equation \( 2x^2 - 6x - 1 = 0 \) using the quadratic formula, follow these steps:
1. Identify the coefficients \( a \), \( b \), and \( c \) from the equation \( ax^2 + bx + c = 0 \).
- Here, \( a = 2 \), \( b = -6 \), and \( c = -1 \).
2. Substitute the coefficients into the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
3. Calculate the discriminant \( b^2 - 4ac \):
\[ (-6)^2 - 4(2)(-1) = 36 + 8 = 44 \]
4. Substitute the discriminant back into the quadratic formula:
\[ x = \frac{6 \pm \sqrt{44}}{4} \]
5. Simplify the expression:
\[ x = \frac{6 \pm 2\sqrt{11}}{4} = \frac{3 \pm \sqrt{11}}{2} \]
6. Write down the solutions:
\[ x = \frac{3 + \sqrt{11}}{2}, \frac{3 - \sqrt{11}}{2} \]
Thus, the solutions to the equation are:
\[ x = \frac{3 + \sqrt{11}}{2}, \frac{3 - \sqrt{11}}{2} \]
### Instructions:
Enter the solutions in the provided answer box, separating them with commas if there is more than one solution.
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