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Advanced Math / Nonlinear functions Difficulty: Medium

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

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Explanation

Choice B is correct. The number that's $8$ more than $x$ can be represented by the expression $x plus 8$ . It's given that the product of $x$ and $x plus 8$ 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: $x equals 10$ and $x = - 18$ . Since $x$ is a positive number, the value of $x$ is $10$ .

Choice A is incorrect. If $x equals 5$ , the product of $x$ and the number that's $8$ more than $x$ would be $left parenthesis 5 right parenthesis left parenthesis 13 right parenthesis$ , 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 $x equals 36$ , the product of $x$ and the number that's $8$ more than $x$ would be $left parenthesis 36 right parenthesis left parenthesis 44 right parenthesis$ , or $1,584$ , not $180$ .