A number and its square

If you add a number to its square, the result is 12. Find all such numbers.

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x = a number
x² = its square

x² + x = 12 {added a number, x, to its square, x², and the result is 12}
x² + x - 12 = 0 {subtracted 12 from each side}
(x + 4)(x - 3) = 0 {factored into two binomials}
x + 4 = 0 or x - 3 = 0 {set each factor equal to zero}
x = -4 or x = 3 {solved each equation for x}
x² = 16 or x² = 9 {squared -4 to get 16 and squared 3 to get 9}

-4 and 16
or
3 and 9 are the numbers

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