SOLUTION: If the product of two consecutive even intergers is 34 larger than their sum, then what are the intergers?

Question 148007: If the product of two consecutive even intergers is 34 larger than their sum, then what are the intergers?
Found 2 solutions by jim_thompson5910, ankor@dixie-net.com:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Remember, consecutive even integers follow the pattern: , , , etc.

So if the "product of two consecutive even intergers is 34 larger than their sum", then we have the equation

Start with the given equation.

Distribute.

Combine like terms

Subtract from both sides. Subtract from both sides.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the first number is either or

And the second number is either or

This means that the two numbers are 6 and 8

OR

the two numbers are -6 and -4

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If the product of two consecutive even integers is 34 larger than their sum, then what are the integers?
;
x(x+2) = x + (x+2) + 34
:
x^2 + 2x = 2x + 36
:
x^2 + 2x - 2x - 36 = 0
:
x^2 - 36 = 0
Factors to:
(x-6)(x+6) = 0
:
x = +6
and
x = -6
:
integers are; 6,8 and -6,-4

RELATED QUESTIONS
If the product of two consecutive even integers is 34 larger than their sum then what... (answered by stanbon)
If the product of two consecutive even integers is 34 larger than their sum then what are (answered by ankor@dixie-net.com)
Solve each problem Consecutive even integers. If the product of two consecutive even... (answered by themathprof)
The Product of two consecutive positive intergers is 1 more than their sum. Find the... (answered by checkley77,Electrified_Levi)
The product of two consecutive positive intergers is 55 more than their sum. Find the... (answered by checkley77)
3)The product of two consecutive intergers is 11 more than their sum. Find the... (answered by rwm)
If the sum of three consecutive odd intergers is 237, then what are the... (answered by Paul)
The product of two consecutive odd intergers is 1 less than four times their sum. Find... (answered by stanbon)
The product of 2 consecutive intergers is 41 more than their sum. find the... (answered by oberobic)