Question

If seven times a number is added to the squares of the number and the result is negative twelve, find the numbers. Explain your reasoning.

Answer 1

let the number be -x
If seven times a number is added to the squares of the number and the result is negative twelve
so, (-x)² + 7(-x) = -12

-x should should be factor of -12
so, factors of -12 = -2, -3, -4, -6, -12

but square of number should not be greater than 7(-x) because answer is in negative
so, possible -x values are -2, -3, -4, -6

if -x = -2
(-2)² + 7(-2) = -12
4 - 14 = -12
-10 is not equal to -12
so, -x is not equal to -2

if -x = -3
(-3)² + 7(-3) = -12
9 - 21 = -12
-12 = -12
so, -x = -3

if -x = -4
(-4)² + 7(-4) = -12
16 - 28 = -12
-12 = -12
so, -x = -4

if -x = -6
(-6)² + 7(-6) = -12
36 - 42 = -12
-6 is not equal to -12
so, -x is not equal to -6

the values of -x that meet the needs of the equation are -3 and -4

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