The product of two consecutive integers is 600. Find the integers.

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Let the consecutive numbers be x and x + 1

As their product is 600

x(x + 1) = 600

=> x^2 + x - 600 = 0

=> x^2 + 25x - 24x - 600 = 0

=> x(x + 25) - 24(x + 25) = 0

=> (x - 24)(x + 25) = 0

=> x = 24 and x = -25

**The consecutive numbers can be 24 and 25 or -24 and -25**

x(x + 1) = 600

distribute the x

x^2 + x = 600

subtract 600

x^2 + x - 600

find factors of -600 that add up to 1

x^2 + 25x - 24x - 600

find the greatest common factors:

x(x + 25) -24 (x + 25)

(x - 24) ( x + 25)

x = 24 x= -25

x(x + 1) = 600

x^2 + x = 600

x^2 + x - 600

x^2 + 25x - 24x - 600

x(x + 25) -24 (x + 25)

(x - 24) ( x + 25)

x = 24 x= -25

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