SOLUTION: if the product of two consecutive integers is decreased by 20 times the greater integer, the result is 442.find the integers.

Question 168019This question is from textbook
: if the product of two consecutive integers is decreased by 20 times the greater integer, the result is 442.find the integers. This question is from textbook

Found 2 solutions by jojo14344, KnightOwlTutor:
Answer by jojo14344(1513) (Show Source): You can put this solution on YOUR website!
Let consecutive inetgers:
= 1st integer
=2nd integer
Condition:
, right? ------------------> Eqn 1
Continuing,

where----
By Pyth. Theorem:

2 values:

Use highlighted DISABLED_event_one= 33, 1st integer; 34 = 2nd inetger (Answer)
Go back Eqn 1 to check:

Thank you,
Jojo
Answer by KnightOwlTutor(293) (Show Source): You can put this solution on YOUR website!
X=first #
x+1=2nd #
The equation is as follows
(x)(x+1)-20(x+1)=442
mulitply the terms to get:
x^2+x-20x-20=442
Combine like terms
x^2-19x-20=442
Add 20 to both sides
x^2-19x=462
Subtract 462 from both sides
x^2-19x-462=0
This is a quadratic eqation or parabola

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=2209 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 33, -14. Here's your graph:

The solutions to this equation is -14,33
Since the number in question is not negative the only solution is 33. Let's check our answer.

(33)(34)-20(34)=442
1,122-680=442

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