Math Snap

STEP 1

1. We are looking for two numbers, say $a$ and $b$, such that their product is $-16$ and their sum is $-6$.
2. The problem is a typical example of factoring a quadratic expression or solving a system of equations involving sum and product.

STEP 2

1. Set up equations based on the given conditions.
2. Solve the system of equations to find the two numbers.

STEP 3

Set up the equations based on the problem statement. We need two numbers $a$ and $b$ such that:
$$a \times b = -16$$ $$a + b = -6$$

STEP 4

To solve for $a$ and $b$, consider possible pairs of factors of $-16$. The factors of $-16$ can be $(-1, 16), (1, -16), (-2, 8), (2, -8), (-4, 4), (4, -4)$.

STEP 5

Check each pair to see which one adds up to $-6$:
- For $(-1, 16)$, the sum is $-1 + 16 = 15$.
- For $(1, -16)$, the sum is $1 - 16 = -15$.
- For $(-2, 8)$, the sum is $-2 + 8 = 6$.
- For $(2, -8)$, the sum is $2 - 8 = -6$.
- For $(-4, 4)$, the sum is $-4 + 4 = 0$.
- For $(4, -4)$, the sum is $4 - 4 = 0$.

Identify the correct pair. The pair $(2, -8)$ satisfies both conditions:
$$2 \times (-8) = -16$$ $$2 + (-8) = -6$$ The two numbers that multiply to $-16$ and add to $-6$ are $2$ and $-8$.