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

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
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twice the number is: 2X
twice the number plus 6 is: 2X + 6
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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
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