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?\
options: \\(x^2 + x + 42 = 0\\), \\(x^2 + x = 42\\), \\(x^2 + 2x + 42 = 0\\), \\(x^2 + 2x = 42\\)

Explanation:

Step1: Define the unknown number

Let the number be $x$. Its square is $x^2$.

Step2: Translate the sum condition

The sum of the number and its square is 42, so set up the equation:
$x^2 + x = 42$

Step3: Verify against options

Match the derived equation to the given choices.

Answer:

$\boldsymbol{x^2 + x = 42}$