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

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,
Louis
Answer by Fermat(136) (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: X�
one half of its square is: X�/2
===============================
twice the number is: 2X
twice the number plus 6 is: 2X + 6
===================================
Equate the two phrases, which you are told are equal,
X�/2 = 2X + 6
multiplying up and moving all terms to the one side, we get a quadratic,
X� - 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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