SOLUTION: How would you put x^2+7x=2x^2+6 in standard form

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Question 825454: How would you put x^2+7x=2x^2+6 in standard form
Found 2 solutions by TimothyLamb, josgarithmetic:
Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
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x^2 + 7x = 2x^2 + 6
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answer:
x^2 - 7x + 6 = 0
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Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
This is a question about Completing The Square.
Simplify what you first can, and then complete the square, simplify more, and put into form of %28x-h%29%5E2%2Bk=0.

x%5E2%2B7x-x%5E2=2x%5E2%2B6-x%5E2
7x=%282-1%29x%5E2%2B6
7x=x%5E2%2B6
0=x%5E2%2B6-7x
x%5E2-7x%2B6=0, general form.

The part, x%5E2-7x, represents the area of a rectangle, x(x-7). You could draw this and figure which region beyond the square portion to cut in half and arrange along another edge, and form an expression for the missing square corner...

The square term to add and subtract is %28-7%2F2%29%5E2=49%2F4;
x%5E2-7x%2B6%2B49%2F4-49%2F4=0
x%5E2-7x%2B49%2F4%2B6-49%2F4=0
%28x%5E2-7x%2B49%2F4%29%2B6-49%2F4=0
%28x-7%2F2%29%5E2%2B6%2A4%2F4-49%2F4=0
%28x-7%2F2%29%5E2%2B%2824-49%29%2F4=0
highlight%28%28x-7%2F2%29%5E2-25%2F4=0%29, DONE.