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.

tomtom Dec 13, 2023

#1**0 **

*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.*

x^{2} = 5x + 270

Get everything on the left x^{2} – 5x – 270 = 0

I couldn't figure out how to factor this, so I used Desmos to plot y = x^{2} – 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.

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Bosco Dec 13, 2023