A number has the property that its square is equal to 84 more than five times the number. Enter all numbers that have this property.

mathlete2008 May 3, 2020

#1**+2 **

So we have a number \(x\) that has this property that makes the following equation true:

\(x^2 = 84 + 5x\)

Changing this to standard quadratic form, we get:

\(x^2 - 5x - 84 = 0\)

This, factored into two binomials, is:

\((x + 7)(x - 12) = 0\)

From this, \(x\) must be either \(\fbox{$-7 \text{ or 12}$}\). I guess those are your numbers :D

CentsLord May 3, 2020

#1**+2 **

Best Answer

So we have a number \(x\) that has this property that makes the following equation true:

\(x^2 = 84 + 5x\)

Changing this to standard quadratic form, we get:

\(x^2 - 5x - 84 = 0\)

This, factored into two binomials, is:

\((x + 7)(x - 12) = 0\)

From this, \(x\) must be either \(\fbox{$-7 \text{ or 12}$}\). I guess those are your numbers :D

CentsLord May 3, 2020