To solve the quadratic expression \(x^2 + 4x - 3 = 0\), we can use the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Here, \(a = 1\), \(b = 4\), and \(c = -3\).

### Step-by-step solution:
1. **Substitute** the values into the quadratic formula:
\[
x = \frac{-4 \pm \sqrt{4^2 - 4(1)(-3)}}{2(1)}
\]
\[
x = \frac{-4 \pm \sqrt{16 + 12}}{2}
\]
\[
x = \frac{-4 \pm \sqrt{28}}{2}
\]

2. **Simplify** the square root:
\[
x = \frac{-4 \pm \sqrt{4 \times 7}}{2}
\]
\[
x = \frac{-4 \pm 2\sqrt{7}}{2}
\]

3. **Simplify the expression**:
\[
x = \frac{-4}{2} \pm \frac{2\sqrt{7}}{2}
\]
\[
x = -2 \pm \sqrt{7}
\]

### Final solutions:
\[
x_1 = -2 + \sqrt{7}
\]
\[
x_2 = -2 - \sqrt{7}
\]

Would you like more details on this solution or have any questions?

Here are some related questions:
1. How do you factor a quadratic equation when factoring is possible?
2. What is the quadratic formula used for solving?
3. How do you complete the square to solve quadratic equations?
4. Can all quadratic equations be solved using the quadratic formula?
5. How can you determine the nature of the roots from the discriminant?

**Tip:** The discriminant (\(b^2 - 4ac\)) in a quadratic equation tells you if the solutions are real or complex. If it's positive, there are two real solutions.

Solve the quadratic equation x² + 4x - 3 using the quadratic formula. Follow a detailed step-by-step solution with explanations of the formula, including the use of discriminant analysis. 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