We are given the quadratic equation:

\[
x^2 - 7x - 8 = 0
\]

To solve for \( x \), 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:

- \( a = 1 \)
- \( b = -7 \)
- \( c = -8 \)

Let's substitute these values into the quadratic formula:

\[
x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(1)(-8)}}{2(1)}
\]

Simplifying the terms inside the square root:

\[
x = \frac{7 \pm \sqrt{49 + 32}}{2}
\]
\[
x = \frac{7 \pm \sqrt{81}}{2}
\]
\[
x = \frac{7 \pm 9}{2}
\]

Now, calculate the two possible values for \( x \):

1. \( x_1 = \frac{7 + 9}{2} = \frac{16}{2} = 8 \)
2. \( x_2 = \frac{7 - 9}{2} = \frac{-2}{2} = -1 \)

Thus, the solutions are:

\[
x = 8 \quad \text{or} \quad x = -1
\]

Do you want more details, or have any questions?

Here are 5 related questions:
1. What is the quadratic formula, and when is it used?
2. How do you determine the number of solutions to a quadratic equation?
3. Can quadratic equations have complex solutions?
4. How would you solve \( x^2 - 7x - 8 = 0 \) by factoring?
5. What are other methods for solving quadratic equations?

**Tip**: Always check the discriminant \( b^2 - 4ac \) to quickly determine the nature of the solutions (real or complex).

Explore the solution to the quadratic equation x^2 - 7x - 8 = 0 using the quadratic formula. This step-by-step guide demonstrates key algebraic concepts, such as solving for roots, and is perfect for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation