Question

What multiplies to -60 and adds to 4

Answer 1

To find two numbers that multiply to -60 and add to 4, we can set up the problem. Let's say the two numbers are \( x \) and \( y \). We need to satisfy the following conditions:

1. \( x \cdot y = -60 \) (their product is -60)
2. \( x + y = 4 \) (their sum is 4)

To find the numbers, we can list the pairs of factors of -60 and check which pair adds up to 4.

The pairs that multiply to -60 are:
- (1, -60)
- (-1, 60)
- (2, -30)
- (-2, 30)
- (3, -20)
- (-3, 20)
- (4, -15)
- (-4, 15)
- (5, -12)
- (-5, 12)
- (6, -10)
- (-6, 10)

Now, we can check their sums:
- \( 1 + (-60) = -59 \)
- \( -1 + 60 = 59 \)
- \( 2 + (-30) = -28 \)
- \( -2 + 30 = 28 \)
- \( 3 + (-20) = -17 \)
- \( -3 + 20 = 17 \)
- \( 4 + (-15) = -11 \)
- \( -4 + 15 = 11 \)
- \( 5 + (-12) = -7 \)
- \( -5 + 12 = 7 \)
- \( 6 + (-10) = -4 \)
- \( -6 + 10 = 4 \)

Thus, the two numbers we are looking for are \( -6 \) and \( 10 \).

So, the final answer is:
\(-6\) and \(10\).