document.write( "Question 87941: solve equation, by making appropriate substitution. \r
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Algebra.Com's Answer #63829 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "solve equation, by making appropriate substitution. \r\n" );
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document.write( "Rule: let U equal the variable part of the second term (without the coefficient)\r\n" );
document.write( "Then UČ will equal the variable part of the first term (without the coefficient)\r\n" );
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document.write( "a)\"x%5E%28-2%29%2Bx%5E%28-1%29-56=0\"\r\n" );
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document.write( "\"U+=+x%5E%28-1%29\", which you see is the variable part of the second term\r\n" );
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document.write( "\"U%5E2=+%28x%5E%28-1%29%29%5E2+=+x%5E%28-2%29\", which is the variable part of the first term \r\n" );
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document.write( "\"x%5E%28-2%29%2Bx%5E%28-1%29-56=0\" becomes\r\n" );
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document.write( "\"U%5E2%2BU%5E2-56=0\"\r\n" );
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document.write( "\"%28U%2B8%29%28U-7%29=0\"\r\n" );
document.write( "\"U%2B8=0\",  \"U-7=0\"\r\n" );
document.write( "\"U=-8\",   \"U=7\"\r\n" );
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document.write( "Now substitute back, using \"U+=+x%5E%28-1%29\",\r\n" );
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document.write( "\"x%5E%28-1%29+=+-8\",  \"x%5E%28-1%29=7\"\r\n" );
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document.write( "Use the definition of a negative exponent to rewrite those:\r\n" );
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document.write( "\"1%2Fx+=+-8\",  \"+1%2Fx+=+7\"\r\n" );
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document.write( "\"1%2Fx+=+%28-8%29%2F1\", \"1%2Fx+=+7%2F1\"\r\n" );
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document.write( "Cross multiply:\r\n" );
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document.write( "\"-8x+=+1\", \"7x+=+1\"\r\n" );
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document.write( "\"x+=+-1%2F8\", \"x+=+1%2F7\"\r\n" );
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document.write( "===================================\r\n" );
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document.write( "b)\"x%5E%282%2F3%29-x%5E%281%2F3%29-12=0\"\r\n" );
document.write( "\"U=x%5E%281%2F3%29\",  the variable part of the second term\r\n" );
document.write( "\"U%5E2=+%28x%5E%281%2F3%29%29%5E2+=+x%5E%282%2F3%29\",  the variable part of the first term \r\n" );
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document.write( "\"x%5E%282%2F3%29-x%5E%281%2F3%29-12=0\" becomes\r\n" );
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document.write( "\"U%5E2-U-12=0\"\r\n" );
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document.write( "\"%28U-4%29%28U%2B3%29=0\"\r\n" );
document.write( "\"U-4=0\",  \"U%2B3=0\"\r\n" );
document.write( "\"U=4\",   \"U=-3\"\r\n" );
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document.write( "Now substitute back, using \"U+=+x%5E%281%2F3%29\",\r\n" );
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document.write( "\"x%5E%281%2F3%29+=+4\",  \"x%5E%281%2F3%29=-3\"\r\n" );
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document.write( "Use the definition of a fractional exponent to rewrite those:\r\n" );
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document.write( "\"root%283%2Cx%29+=+4\",  \"root%283%2Cx%29+=+-3\"\r\n" );
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document.write( "Cubing both sides of both equations:\r\n" );
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document.write( "\"%28root%283%2Cx%29%29%5E3+=+4%5E3\", \"%28root%283%2Cx%29%29%5E3+=+%28-3%29%5E3\"\r\n" );
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document.write( "\"x+=+64\", \"x+=+-27\"\r\n" );
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document.write( "Edwin
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