What two numbers can be multiplied to get 21, and added to get -2?

Xy=21
x+y=-2    ⇒x=-2-y

We solved this equation system by substitution method.
(-2-y)y=21
-2y-y²=21
y²+2y+21=0
We solved this square equation:
y=[-2⁺₋√(4-84)]/2
y=[-2⁺₋√-80] / 2
y=(-2⁺₋4√-5)/2
y=-1⁺₋2√5 i

Therefore.
y₁=-1-2√5 i     ⇒ x₁=-2-y=-1+2√5 i
y₂=-1+2√5 i    ⇒ x₂=-2-y=-1-2√5 i

Solution: we have two solution.
Solution₁
x₁=-1+2√5 i;   y₁=-1-2√5 i
And the other solution is:
solution ₂
x₂=-1+2√5 i; y₂=-1-2√5 i

To check:
Solution₁
(-1+2√5 i)(-1-2√5 i)=1+2√5 i-2√5 i+20=21
(-1+2√5 i)+(-1-2√5 i)=-2

Solution₂
(-1-2√5 i)(-1+2√5 i)=1-2√5 i+2√5 i+20=21
(-1-2√5 i)+((-1+2√5 i)=-2

Therefore:
the solution are complex numbers.
A number is : (-1-2√5 i) and the other number is (-1+2√5 i)
Remember:
i=√-1