Two negative integers have a sum of -10 and a product of 24. Find the two integers.

To find the two integers, let's assume that the first integer is represented by 'x' and the second integer is represented by 'y'.

Given that the sum of the two integers is -10, we can write the equation as follows:
x + y = -10 -- Equation (1)

We are also given that the product of the two integers is 24. We can write the equation as follows:
xy = 24 -- Equation (2)

To solve this system of equations, we can start by solving Equation (1) for one variable and then substitute it into Equation (2).

From Equation (1), we can express 'x' in terms of 'y' as:
x = -10 - y

Substituting this expression for 'x' into Equation (2), we have:
(-10 - y) * y = 24

Expanding and rearranging the equation:
-10y - y^2 = 24
y^2 + 10y + 24 = 0

Now, we can factorize the quadratic equation:
(y + 6)(y + 4) = 0

Setting each factor to zero and solving for 'y':
y + 6 = 0 => y = -6
y + 4 = 0 => y = -4

So, the two possible values for 'y' are -6 and -4.

Substituting these values into Equation (1) to find 'x':
For y = -6:
x + (-6) = -10
x = -4

For y = -4:
x + (-4) = -10
x = -6

Therefore, the two integers are -4 and -6.

put the words into math. They tell you that

x + y = -10
xy = 24

Now, you can do the math and solve the resulting quadratic, but come on. What are the factors of 24 that add up to 10? (or -10 in this case)