document.write( "Question 213121: Please help me to solve this problem : What must be added to $\"4x%5E2+%2B+2x+%2B+1+to+make+it+a+perfect+square%3F+\"$ .Please please please help me. \n" ); document.write( "

Algebra.Com's Answer #161006 by nerdybill(7384) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"4x%5E2+%2B+2x+%2B+1\"$
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\n" ); document.write( "You would look at the terms with 'x's:
\n" ); document.write( " $\"4x%5E2+%2B+2x\"$
\n" ); document.write( "Isolate the $\"x%5E2\"$ term:
\n" ); document.write( " $\"4%28x%5E2+%2B+%282%2F4%29x%29\"$
\n" ); document.write( "Now, to complete the square we need to add a term:
\n" ); document.write( " $\"4%28x%5E2+%2B+%282%2F4%29x+%2B+__+%29\"$
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\n" ); document.write( "That term is ((1/2)b)^2 = [(1/2)(1/2)]^2 = 1/16:
\n" ); document.write( " $\"4%28x%5E2+%2B+%282%2F4%29x+%2B+1%2F16+%29\"$
\n" ); document.write( "Now it is a perfect square:
\n" ); document.write( " $\"4%28x+%2B+1%2F4+%29%5E2\"$
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\n" ); document.write( "So, the term we need to add was 4*(1/16) = 1/4
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\n" ); document.write( "Reviewing:
\n" ); document.write( " $\"4x%5E2+%2B+2x+%2B+1\"$
\n" ); document.write( "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:
\n" ); document.write( " $\"4%28x%5E2+%2B+%282%2F4%29x+%2B+1%2F16%29+%2B+1+-+1%2F4+\"$
\n" ); document.write( " $\"4%28x%5E2+%2B+%282%2F4%29x+%2B+1%2F16%29+%2B+4%2F4+-+1%2F4+\"$
\n" ); document.write( " $\"4%28x%5E2+%2B+%282%2F4%29x+%2B+1%2F16%29+%2B+3%2F4+\"$
\n" ); document.write( " $\"4%28x%2B1%2F4%29%5E2+%2B+3%2F4+\"$
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\n" ); document.write( "This site explains \"completing the square\" quite well:
\n" ); document.write( "http://www.purplemath.com/modules/solvquad3.htm\r
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