To solve the quadratic equation \( x^2 - 121 = 0 \) using the quadratic formula, we'll follow these steps:

1. **Identify coefficients**: The general form of a quadratic equation is \( ax^2 + bx + c = 0 \).
   - Here, \( a = 1 \), \( b = 0 \), and \( c = -121 \).

2. **Quadratic formula**: The quadratic formula is given by:
   \[
   x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   \]
   
3. **Substitute the values**:
   \[
   x = \frac{-0 \pm \sqrt{0^2 - 4(1)(-121)}}{2(1)}
   \]
   \[
   x = \frac{\pm \sqrt{0 + 484}}{2}
   \]
   \[
   x = \frac{\pm \sqrt{484}}{2}
   \]
   \[
   x = \frac{\pm 22}{2}
   \]

4. **Simplify**:
   \[
   x = \frac{22}{2} = 11 \quad \text{or} \quad x = \frac{-22}{2} = -11
   \]

So, the solutions are \( x = 11 \) and \( x = -11 \).

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. What are the properties of a quadratic equation?
2. How do you factor quadratic equations?
3. Can the quadratic formula be used for any quadratic equation?
4. How do you determine the nature of the roots from the discriminant?
5. How do quadratic equations apply to real-world problems?

**Tip:** Always double-check the discriminant (\( b^2 - 4ac \)) before simplifying, as it determines the nature and number of roots (real or complex).

Learn how to solve the quadratic equation x² - 121 using the quadratic formula step-by-step. Understand the application of the quadratic formula to find the roots of quadratic equations. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation