1. Tricky word problem

i am stuck on these 2 problems, any help would be appreciated!

1.If 5 times the square of an integer is decreased by 32 times the number the result is 21. Find the number.

2.the sum of the squares of two positive consecutive integers is 113. Find the numbers.

thanxs!

2. Originally Posted by OnMyWayToBeAMathProffesor
1.If 5 times the square of an integer is decreased by 32 times the number the result is 21. Find the number.

2.the sum of the squares of two positive consecutive integers is 113. Find the numbers.
1. $\displaystyle 5n^2 - 32n = 21$

2.$\displaystyle n^2 + \left( {n + 1} \right)^2 = 113$

3. thanxs

thanks for the formulas but how do i solve them?

4. Originally Posted by OnMyWayToBeAMathProffesor
thanks for the formulas but how do i solve them?
And you are on the way to being a mathematics professor??????

5. someday, but right now i need help, thank you

6. Originally Posted by OnMyWayToBeAMathProffesor
someday, but right now i need help, thank you
Originally Posted by Plato
1. $\displaystyle 5n^2 - 32n = 21$

2.$\displaystyle n^2 + \left( {n + 1} \right)^2 = 113$
Here are some hints.

Get all the terms on one side and make sure everything is expanded fully. the first equation becomes:

$\displaystyle 5n^2 - 32n - 21 = 0$

the second equation becomes:

$\displaystyle 2n^2 + 2n - 112 = 0$

These forms should look familiar, they are quadratic equations. we are expecting integer solutions so you should be able to factor, but if you are lazy, you can use the quadratic formula

Can you take it from here?

7. thanxs

thank you very much, you have helped a lot. also i think factoring is easier than the quadratic formula. Also i thank Plato for the formulas.