To solve the quadratic equation \(x^2 + 7x + 8 = 0\), we can use the **quadratic formula**:

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

For the equation \(x^2 + 7x + 8 = 0\), the coefficients are:
- \(a = 1\)
- \(b = 7\)
- \(c = 8\)

### Step 1: Calculate the discriminant
\[
\Delta = b^2 - 4ac = 7^2 - 4(1)(8) = 49 - 32 = 17
\]

### Step 2: Apply the quadratic formula
\[
x = \frac{-7 \pm \sqrt{17}}{2(1)} = \frac{-7 \pm \sqrt{17}}{2}
\]

### Solution Set
The solution set is:

\[
x_1 = \frac{-7 + \sqrt{17}}{2}, \quad x_2 = \frac{-7 - \sqrt{17}}{2}
\]

These are the exact solutions. You can also approximate them numerically if needed.

Would you like further details on the steps or an approximation of the solutions?

Here are 5 related questions:
1. How do you simplify the discriminant in a quadratic equation?
2. What does the discriminant tell us about the nature of the roots?
3. Can all quadratic equations be solved using factoring?
4. How can you approximate the value of \(\sqrt{17}\) in decimal form?
5. What is the difference between rational and irrational roots?

**Tip:** Always check the discriminant (\(b^2 - 4ac\)) before solving, as it indicates whether the solutions are real, repeated, or complex.

Explore how to solve the quadratic equation x^2 + 7x + 8 using the quadratic formula. This step-by-step solution includes calculating the discriminant and identifying the nature of the roots. Ideal for students in Grades 9-11 looking to strengthen their understanding of algebraic concepts.

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