1963 TMTA High School Algebra I Contest Problem 28

Problem

If we add its square to a certain number, the sum is $72.$ Find the number.

$\text{(A)} \quad 9 \quad \text{(B)} \quad 6 \quad \text{(C)} \quad 36 \quad \text{(D)} \quad -9 \quad \text{(E) NOTA}$

Solution

Let the number be $x.$ Then we have $x^2 + x = 72.$ Solving yields $x = -9$ and $x=8.$

We see that $x=-9$ is an option, so the answer is $\boxed{\text{(D) -9}.}$

(The previous answer was $\boxed{\text{(E) NOTA}}$ , but that is not necessarily true because $x=-9$ is still a possible value for that "certain number".)

1963 TMTA High School Mathematics Contests (Problems)
Preceded by Problem 27	TMTA High School Mathematics Contest Past Problems/Solutions	Followed by Problem 29

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1963 TMTA High School Algebra I Contest Problem 28

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