document.write( "Question 1206414: Question: sqrt(x)-sqrt(3x-3)=1\r
\n" ); document.write( "\n" ); document.write( "My work:
\n" ); document.write( "sqrt(x)-sqrt(3x-3)=1
\n" ); document.write( "(sqrt(x))^2=(1+sqrt(3x-3))^2
\n" ); document.write( "x=(1+sqrt(3x-3))(1+sqrt(3x-3))
\n" ); document.write( "x=1+sqrt(3x-3)+sqrt(3x-3)+(sqrt(3x-3))^2
\n" ); document.write( "x=3x-2+2(sqrt(3x-3))
\n" ); document.write( "(-2x+2)/2=2(sqrt(3x-3))/2
\n" ); document.write( "(-x)^2=(sqrt(3x-3))^2
\n" ); document.write( "x^2=3x-3
\n" ); document.write( "0=x^2+3x-3
\n" ); document.write( "After this step, I get lost. I know the answer is supposed to be 1 but I am not sure where I went wrong or where to go from the last step I took.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #843869 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "Question: sqrt(x)-sqrt(3x-3)=1\r
\n" ); document.write( "\n" ); document.write( "My work:
\n" ); document.write( "sqrt(x)-sqrt(3x-3)=1
\n" ); document.write( "(sqrt(x))^2=(1+sqrt(3x-3))^2
\n" ); document.write( "x=(1+sqrt(3x-3))(1+sqrt(3x-3))
\n" ); document.write( "x=1+sqrt(3x-3)+sqrt(3x-3)+(sqrt(3x-3))^2
\n" ); document.write( "x=3x-2+2(sqrt(3x-3))
\n" ); document.write( "(-2x+2)/2=2(sqrt(3x-3))/2
\n" ); document.write( "(-x)^2=(sqrt(3x-3))^2
\n" ); document.write( "x^2=3x-3
\n" ); document.write( "0=x^2+3x-3
\n" ); document.write( "After this step, I get lost. I know the answer is supposed to be 1 but I am not sure where I went wrong or where to go from the last step I took.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~\r
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document.write( "sqrt(x)-sqrt(3x-3)=1\r\n" );
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document.write( "(sqrt(x))^2 = (1+sqrt(3x-3))^2\r\n" );
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document.write( "x = (1+sqrt(3x-3))(1+sqrt(3x-3))\r\n" );
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document.write( "x = 1+sqrt(3x-3)+sqrt(3x-3)+(sqrt(3x-3))^2\r\n" );
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document.write( "x = 3x-2+2(sqrt(3x-3))\r\n" );
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document.write( "(-2x+2) = 2(sqrt(3x-3))\r\n" );
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document.write( "(-2x+2)/2 = 2(sqrt(3x-3))/2     <<<---===  after this line, your writing was incorrect,\r\n" );
document.write( "                                           so I REPLACED IT. Below is MY writing.\r\n" );
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document.write( "(-x+1)^2 = (sqrt(3x-3))^2\r\n" );
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document.write( "x^2 - 2x + 1 = 3x-3\r\n" );
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document.write( "x^2 - 5x + 4 = 0\r\n" );
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document.write( "(x-4)*(x-1) = 0\r\n" );
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document.write( "So, the two candidates are  x= 4  and  x= 1.\r\n" );
document.write( "Substitute them into the original equation and make sure\r\n" );
document.write( "that x= 4 does not work, while x= 1 works.\r\n" );
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document.write( "ANSWER.  The only solution to the original equation is x= 1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and explained.\r
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