SOLUTION: Please help. Translate into a mathematical equation, solve and answer the question.THE SUM OF AN INTEGER AND ITS SQUARE (THAT INTEGER MULTIPLIED TIMES ITSELF) IS 132. WHAT COULD

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help. Translate into a mathematical equation, solve and answer the question.THE SUM OF AN INTEGER AND ITS SQUARE (THAT INTEGER MULTIPLIED TIMES ITSELF) IS 132. WHAT COULD       Log On


   

Question 192823: Please help.
Translate into a mathematical equation, solve and answer the question.THE SUM OF AN INTEGER AND ITS SQUARE (THAT INTEGER MULTIPLIED TIMES ITSELF) IS 132. WHAT COULD THAT INTEGER BE
Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Please try to not use all caps (it is hard to read).


"The sum of an integer and its square (that integer multiplied times itself) is 132" translates to x%2Bx%5E2=132


x%2Bx%5E2=132 Start with the given equation.


x%2Bx%5E2-132=0 Subtract 132 from both sides.


x%5E2%2Bx-132=0 Rearrange the terms.



Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=1, and c=-132


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%281%29+%2B-+sqrt%28+%281%29%5E2-4%281%29%28-132%29+%29%29%2F%282%281%29%29 Plug in a=1, b=1, and c=-132


x+=+%28-1+%2B-+sqrt%28+1-4%281%29%28-132%29+%29%29%2F%282%281%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1--528+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-132%29 to get -528


x+=+%28-1+%2B-+sqrt%28+1%2B528+%29%29%2F%282%281%29%29 Rewrite sqrt%281--528%29 as sqrt%281%2B528%29


x+=+%28-1+%2B-+sqrt%28+529+%29%29%2F%282%281%29%29 Add 1 to 528 to get 529


x+=+%28-1+%2B-+sqrt%28+529+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-1+%2B-+23%29%2F%282%29 Take the square root of 529 to get 23.


x+=+%28-1+%2B+23%29%2F%282%29 or x+=+%28-1+-+23%29%2F%282%29 Break up the expression.


x+=+%2822%29%2F%282%29 or x+=++%28-24%29%2F%282%29 Combine like terms.


x+=+11 or x+=+-12 Simplify.


So the answers are x+=+11 or x+=+-12


So the number is either 11 or -12.


Note: if you only care about positive numbers, then the answer is 11.


Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let the integer be x.
x+x^2=132
x^2+x-132=0
(x+12)(x-11)=0
x=11, x=-12
.
Ed