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?

Answer 1

For this case we have the following equation:
 $x (x + 1) = 72$
 We can rewrite the expression.
 For this, we first make distributive property:
 $x ^ 2 + x = 72$
 Then, we add -72 on both sides of the equation:
 $x ^ 2 + x - 72 = 72 - 72$
 Rewriting we have:
 $x ^ 2 + x - 72 = 0$
 This is the equation that must be factored and solved for the smallest integer.
 Answer:
 An equation that can be factored and solved for the smaller integer is:
 $x ^ 2 + x - 72 = 0$

Answer 2

Answer:

The smallest integer is 8

Step-by-step explanation:

$x(x+1)=72$

applying distributive law in Right hand side and subtracting 72 from both hand sides we get

$x^2+x-72=0$

Now we are required to find the factors of 72 , such that their difference is 1. The factors are 8 and 9 and 9-8=1. Hence they satisfies our requirements. Now we split the middle term like

$x^2+9x-8x-72=0$

taking x and 8 as GCF from brackets

$x(x+9)-8(x+9)=0$

$(x-8)(x+9)=0$

Hence  

if $(x-8)=0 ; x=8$

if  $(x+9)=0 ; x=-9$

Hence our answer is 8 and 9