SOLUTION: Find two consecutive odd integers such that the sum of their squares is 130.

Question 462751: Find two consecutive odd integers such that the sum of their squares is 130.
Answer by algebrahouse.com(1659) (Show Source): You can put this solution on YOUR website!
"Find two consecutive odd integers such that the sum of their squares is 130."

x = 1st odd integer
x + 2 = 2nd odd integer

x� + (x + 2)� = 130 {sum of their squares is 130}
x� + (x + 2)(x + 2) = 130 {when you square a binomial, multiply it by itself}
x� + x� + 4x + 4 = 130 {used foil method}
2x� + 4x + 4 = 130 {combined like terms}
2x� + 4x - 126 = 0 {subtracted 130 from both sides}
2(x� + 2x - 63) = 0 {factored 2 out}
2(x + 9)(x - 7) = 0 {factored into two binomials}
x + 9 = 0 or x - 7 = 0 {set each factor equal to 0, excluding the 2}
x = -9 or x = 7 {solved each equation for x}
x + 2 = -7 or x + 2 = 9 {substituted -9 and 7, in for x, into x + 2}

-9 and -7, also 7 and 9 are the two consecutive odd integers
www.algebrahouse.com
RELATED QUESTIONS
What are two consecutive odd whole numbers such that the sum of their squares is... (answered by ankor@dixie-net.com)

Find two consecutive odd integers such that the sum of their squares is... (answered by solver91311,MathLover1)

Find two consecutive odd integers such that the sum of their squares is 5834?... (answered by fcabanski)

Find two consecutive odd integers such that the sum of their squares is 802. (answered by ikleyn)

Find two consecutive odd integers such that the sum of their squares is 650. (answered by ikleyn)

The sum of the squares of two consecutive odd integers is 130. Find the... (answered by Alan3354)

the sum of the squares of two consecutive odd postive integers is 130. find the integers (answered by ankor@dixie-net.com)

the sum of the squares of two consecutive odd integers is 130. find the integers. (answered by CubeyThePenguin)

I am thinking of two consecutive odd integers. The sum of their squares is 130. Find... (answered by Alan3354)