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