### 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.

Answered: Image /qna-images/answer/00b35402-6484-432b-a03d-5f51b17f3f82.jpg

.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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Question

### 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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