Two negative integers are 8 units apart on the number line and have a product of 308. Which equation could be used to determine x, the smaller negative integer
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Let the smallest negative integer be = X
Then the larger one is = X + 8
Product of them = 308
X ( X + 8) = 308
X^2 + 8X = 308
X^2 + 8X - 308 = 0
FACTORS of 308 is
2 * 2 * 7 * 11
Now, X^2 + 22X - 14X - 304 = 0
X (X + 22) - 14 (X + 22) = 0
( X + 22) (X - 14) = 0
X = - 22 & X = 14
As the number is negative. Therefore, we should ignore X = 14.
The smallest negative integer is - 22 and the larger one is (- 22 + 8) = - 14.
Then the larger one is = X + 8
Product of them = 308
X ( X + 8) = 308
X^2 + 8X = 308
X^2 + 8X - 308 = 0
FACTORS of 308 is
2 * 2 * 7 * 11
Now, X^2 + 22X - 14X - 304 = 0
X (X + 22) - 14 (X + 22) = 0
( X + 22) (X - 14) = 0
X = - 22 & X = 14
As the number is negative. Therefore, we should ignore X = 14.
The smallest negative integer is - 22 and the larger one is (- 22 + 8) = - 14.
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