Let's call those two factors a and b. So, we have:
a * b = -10
a + b = 9
From the second equation, we can isolate a:
a + b = 9
a + b - b = 9 - b
a = 9 - b
Now, we can use this expression for a in the first equation to find b:
a * b = -10
(9 - b) * b = -10
9b - b² = -10
-b² + 9b + 10 = 0
Notice that we found a second-degree equation. We can either solve it, or just try some pairs of values for a and b to find which one fits the problem.
Let's try integer numbers. The integer pairs of factors of -10 are:
• -1 and 10
,
• 1 and -10
,
• -2 and 5
,
• 2 and -5
Since the sum of the factors is 9, the only possible pair is -1 and 10:
-1 + 10 = 9
Therefore, the factors are -1 and 10.