what multiplied equals -12 and when added equals 4

Question

Cant understand its really complicated to do please help its difficult if you can help thanks thank you 

Answer 1

Xy= -12

 

X+y=4

 

 

Answer 2

You need two numbers that multiply to -12

 

1)   xy = -12

 

The same two numbers add to 4

 

2)   x + y = 4

 

From the 2nd equation subtract y from both sides

x = 4-y

 

Replace x with 4-y in the 1st equation

(4-y)y = -12

4y - y² = -12

 

We can rearrange this

Since we prefer the square term to be positive add y² to both sides

 

4y = y² - 12

 

now subtract 4y from both sides

 

y² - 4y - 12 = 0

 

To factor this we need the factors of -12 that add to -4

Those are (-6)(2) = -12 and  -6+2 = -4

 

y² - 4y - 12 = 0 factors to

 

(y-6)(y+2) = 0

 

y = 6 or y = -2

 

Your two numbers are {6, -2}

*****************************************

 

Note:  From the very beginning we had

xy = -12

x + y = 4

 

This is actually the same point we arrived at through

the long process worked out above...

The numbers are factors of -12 that add to 4

Those numbers are {6, -2}