Question

The sum of a number and its square is 42. Which equation can be used to find the two numbers for which this is true?

x^2 + x = 42
x^2 + 2x = 42
x^2 + x + 42 = 0
x^2 + 2x + 42 = 0

Answer 1

x^2 + x = 42

sum indicates addition
a number = x
it's square = x^2

Answer 2

The correct answer is x^2 + x = 42.

Explanation:

First, we need to declare the unknown, as usual we will use x for the number. Then, the square of the number will be x^2. Following the order of the statement we have that x + x^2 =42. Here we have ‘‘translated’’ the term the sum in the mathematical operation of addition. Moreover, we convert the fact that the sum of a number and its square is 42 in a equality. This is the explanation of the equation x + x^2 =42.

Finally, using that the addition is commutative we have that x^2+x=42.