document.write( "Question 27815: Solve by completing the square.\r
\n" ); document.write( "\n" ); document.write( "x^2=5x+2 \n" ); document.write( "
Algebra.Com's Answer #15150 by sdmmadam@yahoo.com(530)\"\" \"About 
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Solve by completing the square.
\n" ); document.write( "x^2=5x+2
\n" ); document.write( "The golden rule for completing the square method:
\n" ); document.write( "Keep the square term and the term in x on the LHS.
\n" ); document.write( "When the coefficient of x^2 is 1 and the term in x is positive, then
\n" ); document.write( "think of your perfect square in the form
\n" ); document.write( "[x+(1/2)times the coefficient of the term in x]^2
\n" ); document.write( "Then expand using (a+b)^2 formula which gives apart from your two terms on the left an additional quantity that is a constant.
\n" ); document.write( "And if coefficient of x^2 is 1 and the term in x is negative, then
\n" ); document.write( "think of your perfect square in the form
\n" ); document.write( "[x-(1/2)times the coefficient of the term in x]^2
\n" ); document.write( "Then expand using (a-b)^2 formula which gives apart from your two terms on the left an additional quantity that is a constant.
\n" ); document.write( "It is this constant that you have to add to both the sides. You have a perfect square on theLHS and on the RHS you have a sum of the given constant and the constant you have added.
\n" ); document.write( "Simplify the sum on the right.
\n" ); document.write( "Then take square root.
\n" ); document.write( "Do not forget to give (+ or -)sign to the root on the right.
\n" ); document.write( "Transfer the constant term from the left to the right.
\n" ); document.write( "You get two answers:
\n" ); document.write( "x= (the transfered constant+the rootwith the positive sign)
\n" ); document.write( "and x = (the transfered constant+the root with the negative sign))\r
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\n" ); document.write( "\n" ); document.write( "x^2=5x+2
\n" ); document.write( "x^2-5x = 2
\n" ); document.write( "We have (x-5/2)^2 = x^2-5x +25/4
\n" ); document.write( "Therefore we need 25/4 for the LHS to become a perfect square.
\n" ); document.write( "Adding 25/4 to both the sides,
\n" ); document.write( "x^2-5x +25/4= 2+25/4
\n" ); document.write( "That is (x-5/2)^2 = (8+25)/4
\n" ); document.write( "(x-5/2)^2 = (33)/4
\n" ); document.write( "Taking sqroot
\n" ); document.write( "(x-5/2)=+ or -)sqroot(33/4)
\n" ); document.write( "x = [5/2+(or -)sqroot(33/4)]= [5/2+(or -)(1/2)sqroot(33)]\r
\n" ); document.write( "\n" ); document.write( "That is x = (5/2)+(1/2)[(33)^(1/2)]
\n" ); document.write( "And x = (5/2)-(1/2)[(33)^(1/2)]
\n" ); document.write( "OR x = [5+ sqrt(33)]/2 and x = [5- sqrt(33)]/2
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