Ordered Pairs for x and y: How to Solve x2 + 2x + 18 = y2 with Integers?

[spoc21]

Homework Statement

Please find all ordered pairs of integers (x,y) such that x² + 2x + 18 = y²

Homework Equations

x² + 2x + 18 = y²

The Attempt at a Solution

Im not sure on how to begin. I tried square-rooting the expression, to solve for y, turning it into y = \sqrt{x + 2x + 18}. I would greatly appreciate any help to get me started on this problem.

Thanks!

 

[Mark44]

Homework Statement

Please find all ordered pairs of integers (x,y) such that x² + 2x + 18 = y²

Homework Equations

x² + 2x + 18 = y²

The Attempt at a Solution

Im not sure on how to begin. I tried square-rooting the expression, to solve for y, turning it into y = \sqrt{x + 2x + 18}. I would greatly appreciate any help to get me started on this problem.

Thanks!

It might be helpful to complete the square. Then you would have the difference of two squares being equal to -17.

 

[spoc21]

Hey, thanks for the help.
So after this step, do we use trial and error to find the correct solution. I am getting one ordered pair, (9,9), and (-9,-7) after all the math(since x, and y can only be integers). I would really appreciate it if you could confirm this.
Thank you

 

[Mark44]

Those ordered pairs you got aren't solutions. When you completed the square, what did you get for your equation?