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.