To determine the correct equation that can be used to find the number whose sum with its square equals 42, let's go through it step by step:
1. Understanding the problem:
- The problem states that the sum of a number and its square is 42.
2. Expressing the problem mathematically:
- Let's denote the number as [tex]\( x \)[/tex].
- The square of the number is [tex]\( x^2 \)[/tex].
- The sum of the number and its square can be written as [tex]\( x + x^2 \)[/tex].
3. Formulating the equation:
- According to the problem, this sum equals 42. Therefore, we have the equation:
[tex]\[
x + x^2 = 42
\][/tex]
4. Analyzing the given options:
- Option 1: [tex]\( x^2 + x = 42 \)[/tex]
- Option 2: [tex]\( x^2 + 2x = 42 \)[/tex]
- Option 3: [tex]\( x^2 + x + 42 = 0 \)[/tex]
- Option 4: [tex]\( x^2 + 2x + 42 = 0 \)[/tex]
5. Matching our equation with the options:
- Our derived equation [tex]\( x + x^2 = 42 \)[/tex] can be rewritten as [tex]\( x^2 + x = 42 \)[/tex].
- This matches directly with Option 1.
Thus, the correct equation that can be used to find the number for which the sum of the number and its square is 42 is:
[tex]\[
\boxed{x^2 + x = 42}
\][/tex]
