Question

The sum of a number and its square is $132$. How do you find the number?

Answer 1

Hint:As we know that the above given mathematical statement is a word problem question. A word problem is a math question which is written in one sentence or more that requires us to our knowledge to find the equation. There is always some kind of algebraic equation hiding these kinds of problems where we have to solve for them. This type of question is considered a word problem in mathematics.

Complete step by step answer:
Here as per the question we have a number and the square of that number, whose sum is $132$.Let the number be $x$, now applying it on the question the square of the number will be ${x^2}$, So according to the question we have, $x + {x^2} = 132$, we can write it as ${x^2} + x - 132 = 0$.

This is a quadratic equation, to find the value of $x$we need to factorise it by splitting the middle term so that the sum of numbers will be equal to $x$and their product will be equal to $ - 132$ . So we have: ${x^2} + 12x - 11x - 132 = 0$, taking the common factors out,
$x(x + 12) - 11(x + 12) = 0 \\
\Rightarrow (x + 12)(x - 11) = 0$
So we have two factors, solving each $x + 12 = 0$, therefore $x = - 12$ and $x - 11 = 0$, so $x = 11$.Therefore we have two answers i.e. $11$ and $ - 12$.

Hence the required number is $11$ or $ - 12$.

Note:We should keep in mind that for problems like this, it is good to break up the information and visualize how it fits in together.. This is a word problem where significant background information on the problem is presented in ordinary language rather than in mathematical notations. We should identify the problem, gather the information given and we can always cross check our answer but putting the values in the question.