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 \\)

Explanation:

Step1: Define the number

Let the number be \( x \).

Step2: Find the square of the number

The square of the number is \( x^2 \).

Step3: Set up the equation

The sum of the number and its square is \( x + x^2 \), and this sum is equal to 42. So the equation is \( x^2 + x = 42 \).

Answer:

A. \( x^2 + x = 42 \)