document.write( "Question 598721: √(x^2-x)+7=2(x^2-x)-1
\n" ); document.write( "The first part is all in the square root.
\n" ); document.write( "I cannot get the answer at all. I keep comming up with no solution but my teacher says its not right.
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Algebra.Com's Answer #378687 by lwsshak3(11628)\"\" \"About 
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√(x^2-x)+7=2(x^2-x)-1
\n" ); document.write( "let u=(x^2-x)
\n" ); document.write( "√(u+7)=2u-1
\n" ); document.write( "square both sides
\n" ); document.write( "u+7=4u^2-4u+1
\n" ); document.write( "4u^2-5u-6=0
\n" ); document.write( "(4u+3)(u-2)=0
\n" ); document.write( "..
\n" ); document.write( "4u+3=0
\n" ); document.write( "u=-3/4
\n" ); document.write( "x^2-x=3/4
\n" ); document.write( "LCD:4
\n" ); document.write( "4x^2-4x=3
\n" ); document.write( "4x^2-4x-3=0
\n" ); document.write( "(2x-3)(2x+1)=0
\n" ); document.write( "x=3/2
\n" ); document.write( "or
\n" ); document.write( "x=-1/2
\n" ); document.write( "..
\n" ); document.write( "u-2=0
\n" ); document.write( "u=2
\n" ); document.write( "x^2-x=2
\n" ); document.write( "x^2-x-2=0
\n" ); document.write( "(x-2)(x+1)=0
\n" ); document.write( "x=2
\n" ); document.write( "or
\n" ); document.write( "x=-1
\n" ); document.write( "..
\n" ); document.write( "Note: 3/2 and -1/2 may be extraneous roots because we squared both sides. The original is a second degree equation which is only supposed to have 2 roots. You should check by plugging all four roots into the original equation and see which two works.
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