SOLUTION: Write a quadratic equation and solve Two consecutive integers have a product that is 14 less than ten times the smaller integer. Find the integers

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Question 1027955: Write a quadratic equation and solve
Two consecutive integers have a product that is 14 less than ten times the smaller integer. Find the integers
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
x and x+1;
x%28x%2B1%29=-14%2B10x

Some algebra steps
x%5E2%2Bx-10x%2B14=0
x%5E2-9x%2B14=0
%28x-2%29%28x-7%29=0
x must give TWO CONSECUTIVE INTEGERS, according to the description.

The steps there give x=2 and x+1=3.
The steps also there give x=7 and x+1=8.
Those are two different answers. Do both of them work, or does only one of them work?
Test using the original equation.

CHECKING
2%2A3=-14%2B10%2A2
6=-14%2B20
6=20-14=6
next combination
7%2A8=-14%2B10%2A7
56=70-14
56=56
They both work.
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The numbers are either 2 and 3 ; or they are 7 and 8.