Find 2 consecutive integers with a Product of 72

We need two consecutive integers (n) and (n + 1) who have

a product = 72

Setup relational equation:

We need to find two integers, n and n + 1 who have a product of 72
n * (n + 1) = 72

Multiplying through, we get n2 + n = 72

Rearranging the equation we get n2 + n - 72 = 0

Now that it is in Quadratic Format, determine a, b, and c:

a = 1, b = 1, and c = -72

Solution 1 = ½(-b + √b2 - 4ac)

Solution 1 = ½(-1 + √12 - 4 * 1 * -72)

Solution 1 = ½(-1 + √1 - -288)

Solution 1 = ½(-1 + √289)

Solution 1 = ½(-1 + 17)

Solution 1 = ½(16)

Solution 1 = 8

Determine Answers:

Solution 2 = Solution 1 + 1

Solution 2 = 8 + 1

Solution 2 = 9

Also, since the product of 2 negative #'s is positive, another solution is:

Solution 3 = (-1 * 8) * (-1 * 9)

Solution 3 = -1 * 8

Solution 3 = -8

Solution 4 = -1 * 9

Solution 4 = -9

Final Answers:

8, 9, -8, -9

What is the Answer?

8, 9, -8, -9

How does the Consecutive Integer Word Problems Calculator work?

Free Consecutive Integer Word Problems Calculator - Calculates the word problem for what two consecutive integers, if summed up or multiplied together, equal a number entered.
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What 2 formulas are used for the Consecutive Integer Word Problems Calculator?

n + (n + 1) = Sum of Consecutive Integers
n(n + 1) = Product of Consecutive Integers

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What 6 concepts are covered in the Consecutive Integer Word Problems Calculator?

consecutive integer word problemsconsecutive integersintegers that follow each other
n, n + 1integera whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...productThe answer when two or more values are multiplied togethersumthe total amount resulting from the addition of two or more numbers, amounts, or itemsword problemMath problems involving a lengthy description and not just math symbols

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