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I'm thinking of a number. My number has the property that its square is equal to $270$ more than five times the number. Enter all numbers that have this property.

 Dec 13, 2023
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I'm thinking of a number. My number has the property that its square is equal to $270$ more than five times the number. Enter all numbers that have this property.  

 

                                                   x2  =  5x + 270  

 

Get everything on the left           x2 – 5x – 270  =  0  

 

I couldn't figure out how to factor this, so I used Desmos to plot y = x2 – 5x – 270   

which confirmed that the roots are not integers.  Where the parabola crosses the  

x-axis shows the roots are a little smaller than –14.1 and a little larger than +19.1.  

 

You will have to use the quadratic formula if you want exact numbers, if you can   

use exact to describe a number that includes plus/minus the square root of 1105.  

.

 Dec 13, 2023

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