Question

What are the two equations for x^2 + 10 + 16 = 0

Answer 1

To solve the equation \( x^2 + 10x + 16 = 0 \), we can use the quadratic formula, which is given by:

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

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

Now, plug in the values into the quadratic formula:

1. Calculate the discriminant \( b^2 - 4ac \):
\[
b^2 - 4ac = 10^2 - 4 \cdot 1 \cdot 16 = 100 - 64 = 36
\]

2. Substitute the values into the quadratic formula:
\[
x = \frac{-10 \pm \sqrt{36}}{2 \cdot 1}
\]
\[
x = \frac{-10 \pm 6}{2}
\]

This gives us two possible solutions:

1. First solution:
\[
x = \frac{-10 + 6}{2} = \frac{-4}{2} = -2
\]

2. Second solution:
\[
x = \frac{-10 - 6}{2} = \frac{-16}{2} = -8
\]

Thus, the two equations (or solutions) for \( x^2 + 10x + 16 = 0 \) are:
\[
x = -2 \quad \text{and} \quad x = -8
\]