document.write( "Question 366823: Solve by completing the square:
\n" ); document.write( "x2 +1/2x=1
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #261500 by jsmallt9(3758) $\"\"$ $\"About$

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$\"x%5E2+%2B+%281%2F2%29x+=+1\"$
\n" ); document.write( "To complete the square we will start by figuring out 1/2 of the coefficient of x (which is also 1/2). 1/2 of 1/2 is 1/4. We then take this ans square it. 1/4 squared is 1/16. This is what we will add to each side to \"complete the square\":
\n" ); document.write( " $\"x%5E2+%2B+%281%2F2%29x+%2B+1%2F16+=+1+%2B+1%2F16\"$
\n" ); document.write( "On the left we now have a perfect square trinomial. On the right we just add 1 and 1/16:
\n" ); document.write( " $\"%28x+%2B+1%2F4%29%5E2+=+17%2F16\"$
\n" ); document.write( "Now we find the square root of each side:
\n" ); document.write( " $\"sqrt%28%28x+%2B+1%2F4%29%5E2%29+=+sqrt%2817%2F16%29\"$
\n" ); document.write( " $\"abs%28x+%2B+1%2F4%29+=+sqrt%2817%29%2Fsqrt%2816%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"abs%28x+%2B+1%2F4%29+=+sqrt%2817%29%2F4\"$
\n" ); document.write( "We can now remove the absolute value:
\n" ); document.write( " $\"x+%2B+1%2F4+=+0+%2B-+sqrt%2817%29%2F4\"$
\n" ); document.write( "(Note: The extra 0 on the left side is there because Algebra.com's software will not let me use the \"plus or minus\" symbol without having a number or variable in front of it.)
\n" ); document.write( "And last of all we subtract 1/4 (or add a -1/4):
\n" ); document.write( " $\"x+=+-1%2F4+%2B-+sqrt%2817%29%2F4\"$
\n" ); document.write( "which can also be written as:
\n" ); document.write( " $\"x+=+%28-1+%2B-+sqrt%2817%29%29%2F4\"$ \n" ); document.write( "

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