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

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 MULTIPLYIED TIMES ITSELF) IS 132. WHAT COU      Log On


   

Question 192814: Please help.
Translate into a mathematical equation, solve and answer the question.
THE SUM OF AN INTEGER AND ITS SQUARE (THAT INTEGER MULTIPLYIED TIMES ITSELF) IS 132. WHAT COULD THAT INTEGER BE.
Found 2 solutions by checkley77, Earlsdon:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
X+X^2=132
X^2+X-132=0
(X+12)(X-11)=0
X=-12 ANS.
X-11=0
X=11 ANS.
PROOFS:
-12-12^2=132
-12+144=132
132=132
11+11^2=132
11+121=132
132=132

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = the integer in question, then, from the problem description you can write:
n%2Bn%5E2+=+132 Rearrange into a quadratic equation in standard form:
n%5E2%2Bn-132+=+0 Factor this.
%28n-11%29%28n%2B12%29+=+0 Apply the zero product rule.
n-11+=+0 or n%2B12+=+0 so that...
n+=+11 or n+=+-12:
There are two solutions, one positive, (11) and one negative, (-12).
Check:
n%2Bn%5E2+=+132 Substitute n = 11.
11%2B+121+=+132
132+=+132 OK
n%2Bn%5E2+=+132 Substitute n = -12.
-12%2B144+=+132
132+=+132 OK