Question

Find two consecutive integers whose product is 702

Answer 1

Greetings and Happy Holidays!

Let x represent the smaller integer.

We can create an algebraic equation to solve for the numbers:
$(x)(x+1)=702$

Distribute the parenthesis:
$x^2+x=702$

Add -702 to both sides:
$(x^2+x)+(-702)=(702)+(-702)$

$x^2+x-702=0$

Factor the Complex Trinomial:
$x^2-26x+27x-702=0$

$x(x-26)+27(x-26)=0$

$(x-26)(x+27)=0$

Set Factors to Equal 0: 
$x-26=0$

$x=26$

or

$x+27=0$

$x=-27$

The Answer Is:
$\boxed{x=26 x=-27}$

The two consecutive numbers can be either: 26,27 or -27,-26

I hope this helped!
-Benjamin