SOLUTION: Quadratic Equations 10. The sum of the squares of two consecutive integers is 365. Find the integers. Thanks!!!

Question 198390: Quadratic Equations
10. The sum of the squares of two consecutive integers is 365. Find the integers.
Thanks!!!
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Let x = 1st integer, and,,,x+1 = 2nd integer
.
sum of squares is , x^2 + (x+1)^2 = x^2 + x^2 +2x +1 = 2x^2 +2x +1 = 365
.
simplifying, 2x^2 +2x -364 =0, or x^2 +x - 182 =0
.
factoring,,(x+14) (x-13) =0
.
x+14 =0,,, or x= -14 with next integer -13
.
or x-13 = 0, with x=13, and next integer 14
.
both sets check
.

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