Let's continue with algebraic concepts. Here's an example involving solving quadratic equations:

### Example: Solving a Quadratic Equation
Consider the equation:
\[
2x^2 - 4x - 6 = 0
\]

#### Step 1: Simplify the equation
The equation is already simplified, so we can proceed with solving it.

#### Step 2: Use the quadratic formula
The quadratic formula is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Where:
- \(a = 2\) (coefficient of \(x^2\))
- \(b = -4\) (coefficient of \(x\))
- \(c = -6\) (constant term)

Substitute these values into the quadratic formula:
\[
x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(2)(-6)}}{2(2)}
\]
\[
x = \frac{4 \pm \sqrt{16 + 48}}{4}
\]
\[
x = \frac{4 \pm \sqrt{64}}{4}
\]
\[
x = \frac{4 \pm 8}{4}
\]

#### Step 3: Solve for \(x\)
Now solve for the two possible values of \(x\):
1. \(x = \frac{4 + 8}{4} = \frac{12}{4} = 3\)
2. \(x = \frac{4 - 8}{4} = \frac{-4}{4} = -1\)

Thus, the solutions are \(x = 3\) and \(x = -1\).

Would you like a detailed explanation of any of the steps or have questions about other algebraic topics?

Here are some related questions:
1. How do you factor quadratic equations?
2. Can every quadratic equation be solved using the quadratic formula?
3. What are complex roots in a quadratic equation?
4. How do you complete the square to solve a quadratic equation?
5. How does the discriminant in the quadratic formula help determine the nature of the roots?

**Tip:** The discriminant (\(b^2 - 4ac\)) in the quadratic formula tells you whether the roots are real, equal, or complex.

Learn how to solve the quadratic equation 2x^2 - 4x - 6 = 0 using the quadratic formula. This detailed, step-by-step solution covers essential algebraic concepts, including solving quadratic equations and using the discriminant to determine the nature of roots. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation