Consider all possibilities!

Algebra Level 1

600 added to a number x is the same as x squared. What is the sum of all possibilities of x?


The answer is 1.

Hobart Pao by Hobart Pao , 23, USA

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2 solutions

Samuel Li
Apr 5, 2015

The problem can be expressed as 600 + x = x 2 600+x=x^2 , or x 2 − x − 600 = 0 x^2-x-600=0 . By Vieta's formulas, the sum of the roots is − ( − 1 ) 1 = 1 -\frac{(-1)}{1} = \boxed{1} .

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Hobart Pao
Apr 5, 2015

This number x could either be 25 25 because 600 + 25 = 2 5 2 600+25=25^{2} or − 24 -24 because 600 − 24 = ( − 24 ) 2 600-24=\big(-24\big)^{2} . It's just a quadratic equation but just an interesting observation on my part.

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