You can put this solution on YOUR website! xy = -40
Let y = -40/x
x + y = -3
x - 40/x = -3
x²/x - 40/x = -3
(x² - 40)/x = -3
x² - 40 = -3x
x² + 3x - 40 = 0
(x - 5)(x + 8) = 0
x = 5 and x = -8
If x = 5, y = -8.
If x = -8, y = 5.
So, the two integers are 5 and -8.
ANSWER. The numbers are -8 and 5.
Two solutions are possible.
One solution is to guess the answer.
A person familiar with the multiplication table, can do it mentally (inside his mind, without using equations) in 5 seconds.
Alternative solution is algebraic.
x + y = -3 (1)
xy = -40. (2)
From equation (1), express y = -3 - x and substitute to equation (2)
x*(-3-x) = -40.
Simplify it and reduce to the standard form of the quadratic equation
-x^2 - 3x + 40 = 0, or, equivalently,
x^2 + 3x - 40 = 0.
You may solve the last equation EITHER factoring
(x+8)*(x-5) = 0
OR using the quadratic formula
= = = .
It gives you the answer that is placed at the very beginning of my post.
