The equation provided is:

$x^2 - 10x + 16 = 0$

We can solve this quadratic equation using the quadratic formula:

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

Here, the coefficients are:

• $a = 1$
• $b = -10$
• $c = 16$

Step 1: Calculate the discriminant

$\Delta = b^2 - 4ac = (-10)^2 - 4(1)(16) = 100 - 64 = 36$

Step 2: Apply the quadratic formula

$x = \frac{-(-10) \pm \sqrt{36}}{2(1)} = \frac{10 \pm 6}{2}$

Step 3: Compute the two roots

$x_1 = \frac{10 + 6}{2} = \frac{16}{2} = 8$ $x_2 = \frac{10 - 6}{2} = \frac{4}{2} = 2$

Final Answer:

The roots are $x_1 = 8$ and $x_2 = 2$. The largest root is:

$\boxed{8}$

Let me know if you'd like further explanation or more examples!

5 Questions to Expand Understanding:

1. How does the discriminant affect the number of roots in a quadratic equation?
2. What does it mean when the discriminant is negative?
3. Can this quadratic equation be factored directly without the quadratic formula?
4. What are some real-world applications of quadratic equations?
5. How can graphing confirm the roots of this equation?

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