Question 998411
a is one of the numbers
b is the other number
a + b = -35
a * b = -3800
from the first equation, solve for b in terms of a to get b = -a - 35
in the second equation, replace b with -a - 35 to get:
a * (-a - 35) = -3800
remove parentheses to get:
-a^2 - 35a = -3800
add 3800 to both sides of this equation to get:
-a^2 - 35a + 3800 = 0
multiply both sides of this equation by -1 to get:
a^2 + 35a - 3800 = 0
this is a quadratic equation that can be factored to get:
a1 = 46.58002809
a2 = -81.58002809


you know that:


a1 + b1 = -35
a2 + b2 = -35


solve for b1 and b2 to get:


b1 = -81.58002809
b2 = 46.58002809


you get:


a1 = 46.58002809 and b1 = -81.58002809
a2 = -81.58002809 and b2 = 46.58002809


what this says is:


if a = 46.58..., then b = -81.58...
if a = -81.58..., then b = 46.58...


these equaations satisfy the two equations we started with simultaneously.


those equations are:


a + b = -35
a * b = -3800


we can graph these equations and we can then see the solution graphically.


let x = a and y = b,


you get x + y = -35
x * y = -3800


solve for y in both equations to get:


y = -35 - x
y = -3800 / x


the intersections of the graph of these equations is our solution because that point is common to both equations.


the graph look like this:


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