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