https://file.aiquickdraw.com/mathbot/file/1728286944248x27mbmjf.jpg

The equation in the image is:

\[
x^2 - 10x + 16 = 0
\]

This is a quadratic equation. To solve it, we can use the quadratic formula:

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

Here, \(a = 1\), \(b = -10\), and \(c = 16\).

Now, let's calculate the discriminant \(b^2 - 4ac\):

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

Since the discriminant is positive, we have two real solutions. Now, applying the quadratic formula:

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

So the two possible solutions are:

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

Therefore, the solutions are \(x = 8\) and \(x = 2\).

Would you like more details on any step, or do you have any questions?

Here are five related questions:
1. How would the solution change if \(b\) or \(c\) were different?
2. Can this quadratic be factored directly instead of using the quadratic formula?
3. What is the significance of the discriminant value in solving quadratics?
4. How does completing the square compare to using the quadratic formula?
5. What are the applications of solving quadratic equations in real-world scenarios?

**Tip:** Always check the discriminant (\(b^2 - 4ac\)) before using the quadratic formula to determine the nature of the solutions (real or complex).

Solve the quadratic equation x^2 - 10x + 16 = 0

Learn how to solve the quadratic equation x^2 - 10x + 16 using the quadratic formula. The problem covers key algebraic concepts, such as calculating the discriminant and applying the quadratic formula to find real solutions. Suitable for students in Grades 9-10.

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