# SOLUTION: Hi, I could really use some help with this problem: Find a number such that one half of its square is equal to twice the number plus six. Thanks in advance, Louis

Algebra ->  Algebra  -> Sequences-and-series -> SOLUTION: Hi, I could really use some help with this problem: Find a number such that one half of its square is equal to twice the number plus six. Thanks in advance, Louis      Log On

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 Algebra: Sequences of numbers, series and how to sum them Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Sequences-and-series Question 45661: Hi, I could really use some help with this problem: Find a number such that one half of its square is equal to twice the number plus six. Thanks in advance, LouisAnswer by Fermat(127)   (Show Source): You can put this solution on YOUR website!Use the information you are given to build things up. Let the unknown number be X. Its square is: X² one half of its square is: X²/2 =============================== twice the number is: 2X twice the number plus 6 is: 2X + 6 =================================== Equate the two phrases, which you are told are equal, X²/2 = 2X + 6 multiplying up and moving all terms to the one side, we get a quadratic, X² - 4X - 12 = 0 which factorises as, (X-6)(X+2) = 0 therefore: X = 6, X = -2 If we can ignore negative values then there is only one solution, X = 6 =====