Question

the product of two consecutive integers is 72. the equation $x(x + 1) = 72$ represents the situation, where $x$ represents the smaller integer. which equation can be factored and solved for the smaller integer?\
\\(\bigcirc\\ x^2 + x - 72 = 0\\)\
\\(\bigcirc\\ x^2 + x + 72 = 0\\)\
\\(\bigcirc\\ x^2 + 2x - 72 = 0\\)\
\\(\bigcirc\\ x^2 + 2x + 72 = 0\\)

Explanation:

Step1: Expand the given equation

We start with the equation \( x(x + 1)=72 \). Using the distributive property (also known as the distributive law, where \( a(b + c)=ab+ac \)), we multiply \( x \) by each term inside the parentheses. So, \( x\times x+x\times1 = 72 \), which simplifies to \( x^{2}+x = 72 \).

Step2: Rearrange to standard quadratic form

A standard quadratic equation is in the form \( ax^{2}+bx + c = 0 \), where \( a
eq0 \). To get our equation into this form, we subtract 72 from both sides of the equation \( x^{2}+x = 72 \). This gives us \( x^{2}+x - 72=0 \).

Answer:

\( x^{2}+x - 72 = 0 \) (the first option)