# SOLUTION: If twice the square of a positive integer is 12 more than 10 times that integer, what is the integer?

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 Question 69111: If twice the square of a positive integer is 12 more than 10 times that integer, what is the integer?Answer by rmromero(383)   (Show Source): You can put this solution on YOUR website!```What is asked in the problem? What is the integer? Given: Twice the square of a positive integer is 12 more than 10 times that integer. Representation: Let x = the integer Write an Equation.Translate the sentence into mathematical equation Twice the square of a positive integer is 12 more than 10 times that integer. 2x^2 = 10x + 12 Solve the equation. 2x^2 - 10x - 12 = 0 Factor the equation to solve for x. (2x + 2)(x - 6) = 0 Zero product Property. 2x + 2 = 2 or x - 6 = 0 2x = 0 or x = 6 x = 0 or x = 6 Checking: 2x^2 = 10x + 12, x= 0 2(0)^2 = 10(0) + 12 0 = 0 ----------->> True 2x^2 = 10x + 12, x=6 2(6)^2 = 10(6) + 12 72 = 60 + 12 72 = 72 --------->> True Therefore the integer is 0 or 6. ```