To solve the quadratic equation \(x^2 + 4x - 5 = 0\), we can use the **quadratic formula**:

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

For the given equation \(x^2 + 4x - 5 = 0\), the coefficients are:
- \(a = 1\)
- \(b = 4\)
- \(c = -5\)

### Step 1: Plug the values into the quadratic formula:

\[
x = \frac{-4 \pm \sqrt{4^2 - 4(1)(-5)}}{2(1)}
\]

### Step 2: Simplify inside the square root:

\[
x = \frac{-4 \pm \sqrt{16 + 20}}{2}
\]
\[
x = \frac{-4 \pm \sqrt{36}}{2}
\]

### Step 3: Solve the square root:

\[
x = \frac{-4 \pm 6}{2}
\]

### Step 4: Find the two possible values for \(x\):

1. \(x = \frac{-4 + 6}{2} = \frac{2}{2} = 1\)
2. \(x = \frac{-4 - 6}{2} = \frac{-10}{2} = -5\)

Thus, the solutions are:
\[
x = 1 \quad \text{or} \quad x = -5
\]

Would you like more details on any step or have any questions?

Here are 5 related questions you might find helpful:
1. How do you derive the quadratic formula?
2. What are the conditions for a quadratic equation to have real solutions?
3. How do you complete the square for a quadratic equation?
4. Can all quadratic equations be factored, and how do you factor them?
5. How do you graph a quadratic equation?

**Tip**: Always check the discriminant \(b^2 - 4ac\) to determine if the solutions are real, complex, or repeated!

Learn how to solve the quadratic equation x^2 + 4x - 5 = 0 using the quadratic formula. This detailed step-by-step guide covers algebraic concepts, including solving for roots and using the discriminant. Suitable for students in Grades 8-10.

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