SOLUTION: The sum of two consecutive integers is 19 less than their product. Find the integers. Can you please be detailed thank you.

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Question 421708: The sum of two consecutive integers is 19 less than their product. Find the integers. Can you please be detailed thank you.
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Solution: Denote x the first integer and x+1 the consecutive integer.
Their sum is x+(x+1)=2x+1, while their product is x%28x%2B1%29=+x%5E2%2Bx
Base on the given data, we write the equation; %28x%5E2%2Bx%29-%282x%2B1%29=19. We solve this quadratic equation.
+x%5E2%2Bx-2x-1-19=0+
+x%5E2-x-20=0+
+%28x-5%29%28x%2B4%29=0+
{5, -4} are the roots of our equation.
Answer: Our problem have two solutions: The integers that satisfy the problem are:
a) 5 and 6, because 5X6-(5+6)=19.
b) -4 and -3, because, (-4)x(-3)-(-4-3)=12+7=19.