SOLUTION: I am currently working on my summer math packet and I am stuck on this word problem "If 5 times the square of an integer is decreased by 32 times the number the result is 21. Find

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Question 478045: I am currently working on my summer math packet and I am stuck on this word problem "If 5 times the square of an integer is decreased by 32 times the number the result is 21. Find the number."
Found 3 solutions by mananth, MathLover1, MathTherapy:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
let the integer be x
5x^2-32x=21
5x^2-32x-21=0
Find the roots of the equation by quadratic formula

a= 5 b= -32 c= -21

b^2-4ac= 1024 - 420
b^2-4ac= 1444
sqrt%28%091444%09%29= 38
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29

x1=( 32 + 38 )/ 10
x1= 7
x2=( 32 -38 ) / 10
x2= -0.6
Ignore -0.6

7 is the number


Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

let's the number be x
If 5 times the square of an integer 5x%5E2
is decreased by 32 times the number 5x%5E2-32x
the result is 21...->5x%5E2-32x=21....solve quadratic
5x%5E2-32x-21=0...use quadratic formula

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 5%2Ax%5E2-32%2Ax-21=0 ( notice a=5, b=-32, and c=-21)





x+=+%28--32+%2B-+sqrt%28+%28-32%29%5E2-4%2A5%2A-21+%29%29%2F%282%2A5%29 Plug in a=5, b=-32, and c=-21




x+=+%2832+%2B-+sqrt%28+%28-32%29%5E2-4%2A5%2A-21+%29%29%2F%282%2A5%29 Negate -32 to get 32




x+=+%2832+%2B-+sqrt%28+1024-4%2A5%2A-21+%29%29%2F%282%2A5%29 Square -32 to get 1024 (note: remember when you square -32, you must square the negative as well. This is because %28-32%29%5E2=-32%2A-32=1024.)




x+=+%2832+%2B-+sqrt%28+1024%2B420+%29%29%2F%282%2A5%29 Multiply -4%2A-21%2A5 to get 420




x+=+%2832+%2B-+sqrt%28+1444+%29%29%2F%282%2A5%29 Combine like terms in the radicand (everything under the square root)




x+=+%2832+%2B-+38%29%2F%282%2A5%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2832+%2B-+38%29%2F10 Multiply 2 and 5 to get 10


So now the expression breaks down into two parts


x+=+%2832+%2B+38%29%2F10 or x+=+%2832+-+38%29%2F10


Lets look at the first part:


x=%2832+%2B+38%29%2F10


x=70%2F10 Add the terms in the numerator

x=7 Divide


So one answer is

x=7




Now lets look at the second part:


x=%2832+-+38%29%2F10


x=-6%2F10 Subtract the terms in the numerator

x=-3%2F5 Divide


So another answer is

x=-3%2F5


So our solutions are:

x=7 or x=-3%2F5




check our solutions:
x=7
5%2A7%5E2-32%2A7=21
5%2A49-224=21
245-224=21
21=21
or x=-3%2F5
5%2A%28-3%2F5%29%5E2-32%2A%28-3%2F5%29=21
5%2A%289%2F25%29%2B32%2A%283%2F5%29=21
45%2F25%2B96%2F5=21
1.8%2B19.2=21
21=21



Answer by MathTherapy(10845) About Me  (Show Source):
You can put this solution on YOUR website!
I am currently working on my summer math packet and I am stuck on this word problem "If 5 times the square of an integer
is decreased by 32 times the number the result is 21. Find the number."
***********************************
The solutions/roots are: 7 and -+3%2F5. However, as the root/solution/number MUST be an INTEGER, only 7 is VALID/ACCEPTABLE.
The other value, -+3%2F5, is EXTRANEOUS. 

The quadratic equation formula doesn't need to be used, in this case, as the trinomial from the quadratic equation formed:
5N%5E2+-+32N+-+21, is FACTORABLE!

One of the other persons who responded has +-+3%2F5 as one of the solutions. Don't these people pay attention to what they write?
I guess NOT!!!