SOLUTION: The product of two consecutive odd integers is 22 less than the square of the greater integer. Write an equation and find the integers. Thank You!

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Question 717837: The product of two consecutive odd integers is 22 less than the square of the greater integer. Write an equation and find the integers. Thank You!
Answer by algebrahouse.com(1659) About Me  (Show Source):
You can put this solution on YOUR website!
x = first odd integer
x + 2 = second odd integer {consecutive odd integers increase by two}

x(x + 2) = (x + 2)² - 22 {product of two consecutive odd integers is 22 less than square of greater}
x² + 2x = (x + 2)(x + 2) - 22 {used distributive property on left, when you square a binomial, multiply it by itself}
x² + 2x = x² + 4x + 4 - 22 {used foil method on right}
x² + 2x = x² + 4x - 18 {combined like terms}
2x = 4x - 18 {subtracted x² from each side}
-2x = -18 {subtracted 4x from each side}
x = 9 {divided each side by -2}
x + 2 = 11 {substituted 9, in for x, into x + 2}

9 and 11 are the two consecutive odd integers

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