To solve the quadratic equation $x^2 - 10x + 24 = 0$, we can use the quadratic formula:

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

For the equation $x^2 - 10x + 24 = 0$, the coefficients are:

• $a = 1$
• $b = -10$
• $c = 24$

Now, we substitute these values into the quadratic formula:

$x = \frac{-(-10) \pm \sqrt{(-10)^2 - 4(1)(24)}}{2(1)}$

$x = \frac{10 \pm \sqrt{100 - 96}}{2}$

$x = \frac{10 \pm \sqrt{4}}{2}$

$x = \frac{10 \pm 2}{2}$

Now, solve for both roots:

1. $x = \frac{10 + 2}{2} = \frac{12}{2} = 6$
2. $x = \frac{10 - 2}{2} = \frac{8}{2} = 4$

So, the solutions are:

$x = 6 \quad \text{or} \quad x = 4$

Would you like more details on this solution?

Here are 5 related questions to explore:

1. What is the discriminant, and how does it determine the nature of the roots?
2. Can you solve $x^2 - 10x + 24 = 0$ by factoring?
3. How does completing the square work for this equation?
4. How do the roots of a quadratic equation relate to its graph?
5. What happens if the discriminant is negative?

Tip: Always check if a quadratic equation can be factored easily before using the quadratic formula—it can save time!