SOLUTION: two consecutive odd integers such that 55 more than 5 times their sum is equal to their product.

Question 140168: two consecutive odd integers such that 55 more than 5 times their sum is equal to their product.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
:
Let the two consecutive odd integers = x, (x+2)
:
Write an equation for the statement:
"two consecutive odd integers such that 55 more than 5 times their sum is equal to their product."
5(x + (x+2)) + 55 = x(x+2}
:
5(2x+2) + 55 = x^2 + 2x
:
10x + 10 + 55 = x^2 + 2x
:
10x + 65 = x^2 + 2x
Arrange it as a quadratic equation:
x^2 + 2x - 10x - 65 = 0
;
x^2 - 8x - 65 = 0
Factor to
(x-13)(x+5) = 0
Two solutions:
x = 135(x + (x+2) + 55 = x(x+2}
x = -5
:
:
Check for consecutive odd integers: -5 and -3 in the original equation
5(-5 + (-3)) + 55 = -5(-3}
5(-8) + 55 = +15
:
You can check it for x = +13
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