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

Answer:

X * (X +1) = 420

X^2 + X = 420

X^2 + X -420 = 0

X = 20

Step-by-step 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:

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