The given expression is a quadratic equation: 

\[
x^2 + 8x + 7
\]

To solve this quadratic equation, we can factor it, complete the square, or use the quadratic formula. Let's start by factoring.

We are looking for two numbers that multiply to \(7\) (the constant term) and add to \(8\) (the coefficient of \(x\)).

The numbers that work are \(1\) and \(7\):

\[
x^2 + 8x + 7 = (x + 1)(x + 7)
\]

So, the factored form of the quadratic equation is:

\[
(x + 1)(x + 7) = 0
\]

Now, we can find the solutions by setting each factor equal to zero:

1. \(x + 1 = 0 \Rightarrow x = -1\)
2. \(x + 7 = 0 \Rightarrow x = -7\)

Thus, the solutions to the equation \(x^2 + 8x + 7 = 0\) are \(x = -1\) and \(x = -7\).

Would you like more details on the factorization process, or do you have any other questions?

Here are five related questions to expand on this:

1. How would you solve a quadratic equation that can't be factored easily?
2. Can you explain the process of completing the square?
3. How does the quadratic formula apply to solving quadratic equations?
4. What are the properties of the graph of the quadratic function \(y = x^2 + 8x + 7\)?
5. How would you find the vertex of the parabola represented by \(y = x^2 + 8x + 7\)?

**Tip:** Always check your factored equation by expanding it back to the original quadratic to ensure accuracy.

Learn how to solve the quadratic equation x² + 8x + 7 with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring quadratic equations and using the quadratic formula. Suitable for students in Grades 7-9.

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