Product 48 and sum 14 what are the factors

Step-by-step explanation:

Let's write a system.

Let's say that the variables are x and y.

xy=48

x+y=14

Solve for one of the variables, let's say, x.

x=14-y.

Now substitute x into the 1st equation.

(14-y)y=48

Simplify.

-y²+14y=48

Make it into a quadratic equation.

-y²+14y-48=0

Make sure y²'s coefficient is one. Divide everything by -1

y²-14y+48=0

Now factor!

What factors add up to 14 and multiply to 48.

6 and 8!

Since the 2nd term is negative, and the 3rd term is positive, the factors have to be negative.

y²-6y-8y+48=0

Group.

(y²-6y)+(-8y+48)=0

y(y-6)-8(y-6)=0

(y-8)(y-6)=0

y-8=0

y-6=0

y=8 y=6

now let's substitute each y value into y²-14y+48=0

8²-14(8)+48=0

64-112+48=0

0=0. so y=8 checks out!

6²-14(6)+48=0

36-84+48=0

0=0 so y=6 also checks out!

Choose one y value and solve for x, in each equation :

xy=48

x+y=14

8x=48

x+8=14

x=6

x=6

It checks out!

so the factors are

x=6 y=8.

divide by 5

step-by-step explanation:

60/5 = 12