Question

The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring

Answer 1

X * (X +1) = 420

X^2 + X = 420

X^2 + X -420 = 0

X = 20

Explanation:

Answer 2

For this case we have
`20 * 21 = 420.` We must find an equation that allows us to find the smallest value. So:

Let "x" be the variable that represents the smallest number. Thus, "x + 1" represents the consecutive integer. The equation would be given by:

`x * (x + 1) = 420\\x ^ 2 + x = 420\\x ^ 2 + x-420 = 0`

To factor, we must find two numbers that multiply as a result -420 and sum as a result 1.

These numbers are:

`21, -20\\21-20 = 1\\21 * (-20) = -420`

Thus, the factorization is:

`(x-20) (x + 21) = 0`

The roots are:

`x = 20\\x = -21`

Effectively, the smallest integer was found,
`x = 20`.

Answeer:

`x ^ 2 + x-420 = 0\\(x-20) (x + 21) = 0`