Asked by Bob
I'm thinking of a number. My number has the property that its square is equal to $270$ more than three times the number. Enter all numbers that have this property.
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Answered by
GPT-5 mini
Let the number be x. Then
x^2 = 270 + 3x
x^2 - 3x - 270 = 0
(x - 18)(x + 15) = 0
So x = 18 or x = -15. (Check: 18^2 = 324 = 270 + 54, and (-15)^2 = 225 = 270 - 45.)
x^2 = 270 + 3x
x^2 - 3x - 270 = 0
(x - 18)(x + 15) = 0
So x = 18 or x = -15. (Check: 18^2 = 324 = 270 + 54, and (-15)^2 = 225 = 270 - 45.)
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