document.write( "Question 906578: Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)\r
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\n" ); document.write( "\n" ); document.write( "(3)(sqrt 4x − 7) + 2 = (sqrt 9 − x)= 17\r
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\n" ); document.write( "\n" ); document.write( "The answers I got: (8,851/100), (97/10), and (-19/4) all came up incorrect on my homework. \n" ); document.write( "
Algebra.Com's Answer #549948 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\"3sqrt%284x-7%29+%2B+2sqrt%289-x%29=+17\"
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document.write( "Let one of the square roots equal to a letter\r\n" );
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document.write( "Let \"sqrt%289-x%29=A\"\r\n" );
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document.write( "Then we have:\r\n" );
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document.write( "\"3sqrt%284x-7%29+%2B+2A=+17\"\r\n" );
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document.write( "Isolate the remaining radical term on the left\r\n" );
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document.write( "\"3sqrt%284x-7%29+=+17-2A\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"%283sqrt%284x-7%29%29%5E2+=+%2817-2A%29%5E2\"\r\n" );
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document.write( "\"9%284x-7%29=%2817-2A%29%2817-2A%29\"\r\n" );
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document.write( "\"36x-63=289-34A-34A%2B4A%5E2\"\r\n" );
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document.write( "\"36x-63=289-68A%2B4A%5E2\"\r\n" );
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document.write( "\"36x=352-68A%2B4A%5E2\"\r\n" );
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document.write( "Now since  \"A=sqrt%289-x%29\", \"A%5E2=9-x\"\r\n" );
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document.write( "\"36x=352-68sqrt%289-x%29%2B4%289-x%29\"\r\n" );
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document.write( "\"36x=352-68sqrt%289-x%29%2B36-4x\"\r\n" );
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document.write( "\"36x=388-68sqrt%289-x%29-4x\"\r\n" );
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document.write( "Isolate the square root term:\r\n" );
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document.write( "\"68sqrt%289-x%29=388-40x\"\r\n" );
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document.write( "Divide through by 4\r\n" );
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document.write( "\"17sqrt%289-x%29=97-10x\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"%2817sqrt%289-x%29%29%5E2=%2897-10x%29%5E2\"\r\n" );
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document.write( "\"289%289-x%29=%2897-10x%29%2897-10x%29\"\r\n" );
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document.write( "\"2601-289x=9409-970x-970x%2B100x%5E2\"\r\n" );
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document.write( "\"2601-289x=9409-1940x%2B100x%5E2\"\r\n" );
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document.write( "\"0=6808-1651x%2B100x%5E2\"\r\n" );
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document.write( "\"100x%5E2-1651x%2B6808=0\"\r\n" );
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document.write( "That may factor, but it would take longer to\r\n" );
document.write( "factor it than to use the quadratic formula,\r\n" );
document.write( "so I'll just use the quadratic formula:\r\n" );
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document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+\"\r\n" );
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document.write( " \"x+=+%281651+%2B-+sqrt%282601%29+%29%29%2F200+\"\r\n" );
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document.write( " \"x+=+%281651+%2B-+51+%29%2F200+\" \r\n" );
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document.write( "Using the +\r\n" );
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document.write( " \"x+=+%281651+%2B+51+%29%2F200+\"\r\n" );
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document.write( " \"x+=+1702%2F200+\" \r\n" );
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document.write( " \"x+=+851%2F100\"\r\n" );
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document.write( "Using the -\r\n" );
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document.write( " \"x+=+%281651+-+51+%29%2F200+\"\r\n" );
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document.write( " \"x+=+1600%2F200+\" \r\n" );
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document.write( " \"x+=+8\"\r\n" );
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document.write( "So the solutions are \"851%2F100\" and \"8\"\r\n" );
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document.write( "But we must check to see if they are really solutions:\r\n" );
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document.write( "checking \"851%2F100\"\r\n" );
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document.write( "\"3sqrt%284x-7%29+%2B+2sqrt%289-x%29=+17\"\r\n" );
document.write( "\"3sqrt%284%28851%2F100%29-7%29+%2B+2sqrt%289-851%2F100%29=+17\"\r\n" );
document.write( "\"3sqrt%28851%2F25-7%29+%2B+2sqrt%289-851%2F100%29=+17\"\r\n" );
document.write( "\"3sqrt%28851%2F25-175%2F25%29+%2B+2sqrt%28900%2F100-851%2F100%29=+17\"\r\n" );
document.write( "\"3sqrt%28676%2F25%29+%2B+2sqrt%2849%2F100%29=+17\"\r\n" );
document.write( "\"3%2826%2F5%29%2B2%287%2F10%29=17\"\r\n" );
document.write( "\"78%2F5%2B14%2F10=17\"\r\n" );
document.write( "\"156%2F10%2B14%2F10=17\"\r\n" );
document.write( "\"170%2F10=17\"\r\n" );
document.write( "\"17=17\"\r\n" );
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document.write( "checking \"8\"\r\n" );
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document.write( "\"3sqrt%284x-7%29+%2B+2sqrt%289-x%29=+17\"\r\n" );
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document.write( "\"3sqrt%284%2A8-7%29+%2B+2sqrt%289-8%29=+17\"\r\n" );
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document.write( "\"3sqrt%2832-7%29%2B2sqrt%281%29=17\"\r\n" );
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document.write( "\"3sqrt%2825%29%2B2%281%29=17\"\r\n" );
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document.write( "\"3%2A5%2B2=17\"\r\n" );
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document.write( "\"15%2B2-17\"\r\n" );
document.write( "\"17=17\"\r\n" );
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document.write( "They both check.\r\n" );
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document.write( "Edwin
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