The equation you provided is:

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

We can solve this quadratic equation using the quadratic formula or by completing the square, but let's check if it factors easily first.

### 1. Factoring the quadratic equation
We are looking for two numbers that multiply to \( 16 \) and add to \( 10 \). However, since no such pair exists, factoring is not a straightforward option. We’ll use the quadratic formula instead.

### 2. Solving using the quadratic formula

The quadratic formula is:

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

For the equation \(x^2 + 10x + 16 = 0\), the coefficients are:
- \(a = 1\)
- \(b = 10\)
- \(c = 16\)

Substitute these into the quadratic formula:

\[
x = \frac{-10 \pm \sqrt{10^2 - 4(1)(16)}}{2(1)}
\]
\[
x = \frac{-10 \pm \sqrt{100 - 64}}{2}
\]
\[
x = \frac{-10 \pm \sqrt{36}}{2}
\]
\[
x = \frac{-10 \pm 6}{2}
\]

### 3. Calculate the two possible solutions:
- \(x = \frac{-10 + 6}{2} = \frac{-4}{2} = -2\)
- \(x = \frac{-10 - 6}{2} = \frac{-16}{2} = -8\)

Thus, the solutions are:
\[
x = -2 \quad \text{or} \quad x = -8
\]

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

Here are 5 related questions for further practice:
1. Solve \(x^2 + 8x + 15 = 0\) using the quadratic formula.
2. What are the solutions to \(x^2 + 6x + 9 = 0\)?
3. How would you factor \(x^2 + 12x + 36 = 0\)?
4. Solve \(2x^2 + 4x - 6 = 0\).
5. Explain how the discriminant affects the nature of solutions in a quadratic equation.

**Tip**: The discriminant \(b^2 - 4ac\) determines if a quadratic equation has real or complex solutions. If it’s positive, you get two real solutions!

Learn how to solve the quadratic equation x^2 + 10x + 16 using the quadratic formula. This step-by-step solution covers important algebraic concepts and explains the use of the quadratic formula for students in Grades 8-10.

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