The product of a positive number x and the number that is 8 more than x is 180 . What

Question

The product of a positive number x and the number that is 8 more than x is 180 . What is the value of x ?

Accepted Answer

Choice B is correct. The number that's 8 more than x can be represented by the expression x + 8 . It's given that the product of x and x + 8 is 180 , so it follows that x x + 8 = 180 , or x 2 + 8 x = 180 . Subtracting 180 from each side of this equation yields x 2 + 8 x - 180 = 0 . Factoring the left-hand side of this equation yields x - 10 x + 18 = 0 . Applying the zero product property to this equation yields two solutions: x = 10 and x = - 18 . Since x is a positive number, the value of x is 10 . Choice A is incorrect. If x = 5 , the product of x and the number that's 8 more than x would be 5 13 , or 65 , not 180 . Choice C is incorrect. This is the value of the number that's 8 more than x , not the value of x . Choice D is incorrect. If x = 36 , the product of x and the number that's 8 more than x would be 36 44 , or 1,584 , not 180 .

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