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

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

For the given equation:

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

Substituting these values into the quadratic formula:

\[
x = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(1)(7)}}{2(1)}
\]
\[
x = \frac{8 \pm \sqrt{64 - 28}}{2}
\]
\[
x = \frac{8 \pm \sqrt{36}}{2}
\]
\[
x = \frac{8 \pm 6}{2}
\]

This gives us two possible solutions:

\[
x_1 = \frac{8 + 6}{2} = \frac{14}{2} = 7
\]
\[
x_2 = \frac{8 - 6}{2} = \frac{2}{2} = 1
\]

So, the solutions are \( x = 7 \) and \( x = 1 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How can you derive the quadratic formula?
2. What is the significance of the discriminant in a quadratic equation?
3. Can you solve a quadratic equation by factoring instead of using the quadratic formula?
4. How does the quadratic formula apply to complex roots?
5. What are some real-life applications of quadratic equations?

**Tip:** Always check if a quadratic equation can be factored easily before applying the quadratic formula, as factoring might be faster.

Learn how to solve the quadratic equation x^2 - 8x + 7 = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic formula. Suitable for students in Grades 7-9.

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