The problem presented is to solve the quadratic equation:

$x^2 + 7x = 8$

First, let’s rewrite this equation in standard form:

$x^2 + 7x - 8 = 0$

This is a quadratic equation of the form $ax^2 + bx + c = 0$, where $a = 1$, $b = 7$, and $c = -8$. We can solve this equation using the quadratic formula:

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

Substitute the values of $a$, $b$, and $c$:

$x = \frac{-7 \pm \sqrt{(7)^2 - 4 \cdot 1 \cdot (-8)}}{2 \cdot 1}$ $x = \frac{-7 \pm \sqrt{49 + 32}}{2}$ $x = \frac{-7 \pm \sqrt{81}}{2}$ $x = \frac{-7 \pm 9}{2}$

Now, solve for the two possible values of $x$:

1. $x = \frac{-7 + 9}{2} = \frac{2}{2} = 1$
2. $x = \frac{-7 - 9}{2} = \frac{-16}{2} = -8$

The solutions are $x = 1$ and $x = -8$.

Answer:

The correct answer is C: $x = 1$; $x = -8$.

Would you like further details, or do you have any questions?

Here are some related questions for additional practice:

1. How would you solve a quadratic equation using factoring?
2. What is the process of completing the square, and how is it used to solve quadratics?
3. How can you determine the nature of the roots of a quadratic equation using the discriminant?
4. How do you apply the quadratic formula to an equation with complex roots?
5. How does the graph of a quadratic equation relate to its solutions?

Tip: Always check if a quadratic equation can be factored easily before applying the quadratic formula. This can sometimes save time and simplify the solution process.