Question 213121
{{{4x^2 + 2x + 1}}}
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You would look at the terms with 'x's:
{{{4x^2 + 2x}}}
Isolate the {{{x^2}}} term:
{{{4(x^2 + (2/4)x)}}}
Now, to complete the square we need to add a term:
{{{4(x^2 + (2/4)x + __ )}}}
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That term is ((1/2)b)^2 = [(1/2)(1/2)]^2 = 1/16:
{{{4(x^2 + (2/4)x + 1/16 )}}}
Now it is a perfect square:
{{{4(x + 1/4 )^2}}}
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So, the term we need to add was 4*(1/16) = 1/4
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Reviewing:
{{{4x^2 + 2x + 1}}}
Since we need to add 1/4 to the x-terms, we need to subtract the same amount from the equation to keep it balance:
{{{4(x^2 + (2/4)x + 1/16) + 1 - 1/4 }}}
{{{4(x^2 + (2/4)x + 1/16) + 4/4 - 1/4 }}}
{{{4(x^2 + (2/4)x + 1/16) + 3/4 }}}
{{{4(x+1/4)^2 + 3/4 }}}
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This site explains "completing the square" quite well:
http://www.purplemath.com/modules/solvquad3.htm