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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.

 May 3, 2020

Best Answer 

 #1
avatar+300 
+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

 May 3, 2020
 #1
avatar+300 
+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
 #2
avatar+87 
0

Thank you!

 May 4, 2020

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