An integers is 2 less than twice another. if the product of the integers is 220, then find the integers.

Givens

Let one of the integers = x

Let one of the integers = y

y = 2x - 2

x * y = 220

Solution

x * (2x - 2) = 220   Remove the brackets.

2x^2 - 2x = 220    Divide through by 2. It makes what you are looking for easier.

x^2 - x = 110           Subtract 110 from both sides.

x^2 - x - 110 = 0      You need two numbers that are close together and multiply to 110.  10 and 11 should do it in some form.

x^2 - x - 110 = 0

(x    11)(x   10) = 0 These are of opposite signs. One is minus the other is plus but which is which. Since you have - x in the middle the 11 must be minus and the 10 plus.

(x - 11)(x + 10) = 0

So you have 2 answers

x - 11 = 0

x = 11

So y would be 2*11 - 2 = 20

or

x + 10 =0

x = - 10

and y = 2*-10 - 2 = - 20 - 2 = - 22

Check

if x = 11 then

y = 2x - 2

y = 2*11 - 2

y = 22 - 2

y = 20

20 * 11 = 220

x =-10

y = - 22

(-10)(-22) = 220 and this checks.

step-by-step explanation: