what two numbers would multiply to -1040 & add up to be 14

Let's use x and y for the two numbers and set up equations:

x*y = -1040

x + y = 14

x + y = 14

y = 14 - x

Let's substitute that into the first equation

x*(14 - x) = -1040.

14x - x^2 = -1040.

Move over everything to the write to get:

x^2 - 14x - 1040 = 0.

Now, let's use the quadratic formula to solve this:

http://www.math.com/students/calculators/source/quadratic.htm is a quick way to get the numbers.

We get x = 40 and x = -26

So, our two numbers are -26 and 40.

what two numbers would multiply to -1040 & add up to be 14

$$\\x^2+px+q=0 \quad
\begin{array}{rcrcr}
x_1+x_2&=&14&=&-p\\
x_1x_2&=&-1040&=&q\\
\end{array} \quad
x^2-14x-1040=0$$

$$\underbrace{
\left(
x-\frac{14}{2}
\right)^2}
_{x^2-14x+\frac{14^2}{4}}
-\frac{14^2}{4}-1040=0$$

$$\left(
x-7\right)^2=1040 + 49$$

$$\left(
x-7\right)^2=1089 \quad | \quad \pm \sqrt{}$$

$$x-7=\pm 33$$

$$x_1 = 33 + 7 = 40$$

$$x_2 = -33 + 7 = -26$$