document.write( "Question 147430: Solve by completing the square:
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document.write( "x^2 + 6x + 1 = 0
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Algebra.Com's Answer #107810 by nerdybill(7384)![]() ![]() You can put this solution on YOUR website! This site describes it quite well: \n" ); document.write( "http://www.purplemath.com/modules/solvquad3.htm \n" ); document.write( ". \n" ); document.write( "x^2 + 6x + 1 = 0 \n" ); document.write( ". \n" ); document.write( "First, isolate the x's -- so, subtract 1 from both sides: \n" ); document.write( "x^2 + 6x = -1 \n" ); document.write( ". \n" ); document.write( "Next, look at the coefficient associated with the x term (6). Divide this by 2 and square it to get 9. \n" ); document.write( ". \n" ); document.write( "So, we ADD 9 to both sides: \n" ); document.write( "x^2 + 6x + 9 = -1 + 9 \n" ); document.write( ". \n" ); document.write( "Now, we factor the left side and combine the right to get: \n" ); document.write( "(x+3)(x+3) = 8 \n" ); document.write( "(x+3)^2 = 8 \n" ); document.write( ". \n" ); document.write( "To solve: \n" ); document.write( "(x+3)^2 = 8 \n" ); document.write( "Take the square root of both sides: \n" ); document.write( "x + 3 = (+-)sqrt(8) \n" ); document.write( "x = (+-)sqrt(8) - 3 \n" ); document.write( "x = (+-)2sqrt(2) - 3 \n" ); document.write( ". \n" ); document.write( "Note: the (+-) means \"plus or minus\" \n" ); document.write( " \n" ); document.write( " |