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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**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.
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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