**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.

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,...

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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.

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