For this case we have [tex]20 * 21 = 420.[/tex] 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:
[tex]x * (x + 1) = 420\\x ^ 2 + x = 420\\x ^ 2 + x-420 = 0[/tex]
To factor, we must find two numbers that multiply as a result -420 and sum as a result 1.
These numbers are:
[tex]21, -20\\21-20 = 1\\21 * (-20) = -420[/tex]
Thus, the factorization is:
[tex](x-20) (x + 21) = 0[/tex]
The roots are:
[tex]x = 20\\x = -21[/tex]
Effectively, the smallest integer was found,[tex]x = 20[/tex].
Answeer:
[tex]x ^ 2 + x-420 = 0\\(x-20) (x + 21) = 0[/tex]
