Question

The sum of the squares of two consecutive negative integer is 61. Find the smaller of the two integers. Help pls

Answer 1

let x equal the smaller of the 2 integers

then the next consecutive negative integer would be "x+1"

we know the square of the 2 numbers is equal to 61

(x)^2+(x+1)^2=61

just solve for x (remember that x needs to be negative)

Answer 2

Are you able to proceed?

Answer 3

Well I got 2x^2+4x-57=0
After I have foiled and added now I'm stuck :/

Answer 4

What do I do?

Answer 5

quadratic equation

Answer 6

You need to redo your foil tho

Answer 7

Review your result of (x+1)^2

Answer 8

The quadratic that you need to solve is this:
\[2n ^{2}-2n-60=0\]

Answer 9

Lol yeah guys sorry i just checked my work your right :)

Answer 10

Yes, that is what you are striving for. You can simplify by dividing all terms by 2 getting\[n ^{2}+n - 30 = 0\]after correcting the sign of 2n in kropot72 post.

Answer 11

Thank you!

Answer 12

You can use the quadratic, but if you recognize it, this factors quite nicely

Answer 13

Now factor and solve.

Answer 14

Have you factored it yet?

Answer 15

Yes, I see that the question is now closed. Completeidiot gave excellent guidance. We all tried, I hope some understanding was imparted.