Explanation:
x + y = 12
x × y = -360
we need to transform one equation into an identity of one variable being expressed by the other variable.
e.g. the first equation gives us
x = -y + 12
and then we use that in the second equation :
(-y + 12) × y = -360
-y² + 12y = -360
y² - 12y - 360 = 0
the general solution for such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = y
a = 1
b = -12
c = -360
y = (12 ± sqrt(144 - 4×1×-360))/2 =
= (12 ± sqrt(144 + 1440))/2 = (12 ± sqrt(1584))/2 =
= 6 ± sqrt(1584/4) = 6 ± sqrt(396) = 6 ± sqrt(36×11) =
= 6 ± 6×sqrt(11)
y1 = 6 + 6×sqrt(11) = 25.89974874...
y2 = 6 - 6×sqrt(11) = -13.89974874...
x1 = -y1 + 12 = -13.89974874...
x2 = -y2 + 12 = 25.89974874...
so, we see, they are interchangeable.
the solution is either
x = 25.89974874...
and
y = -13.89974874...
or
x = -13.89974874...
and
y = 25.89974874...