Use the quadratic formula to solve for x. 6x²-9x+1=0 (If there is more than one solution, separate them with commas.) Xx= Explanation 57°F Mostly cloudy Check 0/6 0° 00 X 0,0.... a hp ©2022 McGraw Hill LLC. All Rights Re
Use the quadratic formula to solve for x. 6x²-9x+1=0 (If there is more than one solution, separate them with commas.) Xx= Explanation 57°F Mostly cloudy Check 0/6 0° 00 X 0,0.... a hp ©2022 McGraw Hill LLC. All Rights Re
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,...
Related questions
Question
![**Educational Content:**
---
**Topic: Solving Quadratic Equations Using the Quadratic Formula**
---
**Objective:**
Learn how to apply the quadratic formula to solve quadratic equations and obtain exact solutions.
**Example Problem:**
Solve the equation \(6x^2 - 9x + 1 = 0\).
**Step-by-Step Solution:**
1. **Identify the coefficients** in the quadratic equation \(ax^2 + bx + c = 0\). For this equation:
- \(a = 6\)
- \(b = -9\)
- \(c = 1\)
2. **Apply the Quadratic Formula:**
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
3. **Calculate the Discriminant:**
\[
b^2 - 4ac = (-9)^2 - 4 \times 6 \times 1 = 81 - 24 = 57
\]
4. **Solve for \(x\):**
\[
x = \frac{-(-9) \pm \sqrt{57}}{2 \times 6}
\]
\[
x = \frac{9 \pm \sqrt{57}}{12}
\]
**Note:** If there are multiple solutions, they should be expressed separately with commas in between.
**Answer Box:**
- Type the calculated \(x\) values here to submit.
---
**Interactive Features:**
- **Explanation Button:** Provides a detailed explanation for each step.
- **Check Button:** Verifies the solution entered.
This exercise helps build proficiency in solving quadratic equations and understanding how solutions are derived using the quadratic formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93976936-9bd0-47c5-8a3c-e89a2ab20129%2F3d96dc1e-ffae-4bc3-affe-684ffbb438fa%2Flh5bdq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content:**
---
**Topic: Solving Quadratic Equations Using the Quadratic Formula**
---
**Objective:**
Learn how to apply the quadratic formula to solve quadratic equations and obtain exact solutions.
**Example Problem:**
Solve the equation \(6x^2 - 9x + 1 = 0\).
**Step-by-Step Solution:**
1. **Identify the coefficients** in the quadratic equation \(ax^2 + bx + c = 0\). For this equation:
- \(a = 6\)
- \(b = -9\)
- \(c = 1\)
2. **Apply the Quadratic Formula:**
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
3. **Calculate the Discriminant:**
\[
b^2 - 4ac = (-9)^2 - 4 \times 6 \times 1 = 81 - 24 = 57
\]
4. **Solve for \(x\):**
\[
x = \frac{-(-9) \pm \sqrt{57}}{2 \times 6}
\]
\[
x = \frac{9 \pm \sqrt{57}}{12}
\]
**Note:** If there are multiple solutions, they should be expressed separately with commas in between.
**Answer Box:**
- Type the calculated \(x\) values here to submit.
---
**Interactive Features:**
- **Explanation Button:** Provides a detailed explanation for each step.
- **Check Button:** Verifies the solution entered.
This exercise helps build proficiency in solving quadratic equations and understanding how solutions are derived using the quadratic formula.
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