SOLUTION: the product of two consecutive even integers decreased by seven times the greater integer is 70. find the two integers

Question 140412: the product of two consecutive even integers decreased by seven times the greater integer is 70. find the two integers
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let the two consecutive integers be: x, (x+2)
:
Write an equation for the statement:
"the product of two consecutive even integers decreased by seven times the greater integer is 70."
x(x+2) - 7(x+2) = 70
:
x^2 + 2x - 7x - 14 = 70
:
x^2 - 5x - 14 - 70 = 0
:
x^2 - 5x - 84 = 0
Factors to:
(x-12)(x+7) = 0
Two solutions:
x = -7
x = +12
:
find the two integers:
:
The even solutions: 12, 14
:
:
Check solution using the statement:
"the product of two consecutive even integers decreased by seven times the greater integer is 70"
12 * 14 - 7 * 14 =
168 - 98 = 70; confirms the solution

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