To find the correct equation that could be solved to determine the value of the smaller number [tex]\( x \)[/tex], let's analyze the problem step by step.
1. We are given that the product of two numbers is 550. These two numbers are [tex]\( x \)[/tex] and [tex]\( x + 3 \)[/tex].
2. To formulate an equation from this information, we write the product of these two numbers as an equation:
[tex]\[
x \cdot (x + 3) = 550
\][/tex]
3. Next, we need to simplify this equation to a standard quadratic form. We do this by distributing [tex]\( x \)[/tex] across the term [tex]\( (x + 3) \)[/tex]:
[tex]\[
x^2 + 3x = 550
\][/tex]
4. This equation [tex]\( x^2 + 3x = 550 \)[/tex] is now in the form of a standard quadratic equation [tex]\( ax^2 + bx + c = 0 \)[/tex], where the quadratic term is [tex]\( x^2 \)[/tex], the linear term is [tex]\( 3x \)[/tex], and the constant term is [tex]\( -550 \)[/tex] since we would usually move all terms to one side to set the equation to zero:
[tex]\[
x^2 + 3x - 550 = 0
\][/tex]
Among the given options, D. [tex]\( x^2 + 3x = 550 \)[/tex] is the equation we simplified to reach and is thus the correct equation that could be solved to find the value of the smaller number, [tex]\( x \)[/tex].
Thus, the correct answer is:
D. [tex]\( x^2 + 3x = 550 \)[/tex]
