document.write( "Question 161945: (a) (4x+2)(2x) = 32\r
\n" ); document.write( "\n" ); document.write( "(b) (3x+2)(9x+3) = 81\r
\n" ); document.write( "\n" ); document.write( "(c) log (x-3) + log (x) = 1\r
\n" ); document.write( "\n" ); document.write( "(d) log2 (x2 – 6x) = 3 + log2 (1-x)
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Algebra.Com's Answer #119335 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
I'll do the first two to get you started\r
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\n" ); document.write( "\n" ); document.write( "\"%284x%2B2%29%282x%29+=+32+\" Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "\"8x%5E2%2B4x+=+32+\" Distribute\r
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\n" ); document.write( "\n" ); document.write( "\"8x%5E2%2B4x-32=0\" Subtract 32 from both sides\r
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\n" ); document.write( "\n" ); document.write( "Notice we have a quadratic equation in the form of \"ax%5E2%2Bbx%2Bc\" where \"a=8\", \"b=4\", and \"c=-32\"\r
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\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for x\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\" Start with the quadratic formula\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-%284%29+%2B-+sqrt%28+%284%29%5E2-4%288%29%28-32%29+%29%29%2F%282%288%29%29\" Plug in \"a=8\", \"b=4\", and \"c=-32\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-4+%2B-+sqrt%28+16-4%288%29%28-32%29+%29%29%2F%282%288%29%29\" Square \"4\" to get \"16\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-4+%2B-+sqrt%28+16--1024+%29%29%2F%282%288%29%29\" Multiply \"4%288%29%28-32%29\" to get \"-1024\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-4+%2B-+sqrt%28+16%2B1024+%29%29%2F%282%288%29%29\" Rewrite \"sqrt%2816--1024%29\" as \"sqrt%2816%2B1024%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-4+%2B-+sqrt%28+1040+%29%29%2F%282%288%29%29\" Add \"16\" to \"1024\" to get \"1040\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-4+%2B-+sqrt%28+1040+%29%29%2F%2816%29\" Multiply \"2\" and \"8\" to get \"16\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-4+%2B-+4%2Asqrt%2865%29%29%2F%2816%29\" Simplify the square root (note: If you need help with simplifying square roots, check out this solver) \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-4%2B4%2Asqrt%2865%29%29%2F%2816%29\" or \"x+=+%28-4-4%2Asqrt%2865%29%29%2F%2816%29\" Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-1%2Bsqrt%2865%29%29%2F%284%29\" or \"x+=+%28-1-sqrt%2865%29%29%2F%284%29\" Reduce\r
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\n" ); document.write( "\n" ); document.write( "So the answers are \"x+=+%28-1%2Bsqrt%2865%29%29%2F%284%29\" or \"x+=+%28-1-sqrt%2865%29%29%2F%284%29\"\r
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\n" ); document.write( "\n" ); document.write( "which approximate to \"x=1.766\" or \"x=-2.266\" \r
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\n" ); document.write( "\n" ); document.write( "\"%283x%2B2%29%289x%2B3%29+=+81+\" Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "\"27x%5E2%2B27x%2B6+=+81+\" FOIL\r
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\n" ); document.write( "\n" ); document.write( "\"27x%5E2%2B27x%2B6-81=0\" Subtract 81 from both sides\r
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\n" ); document.write( "\n" ); document.write( "\"27x%5E2%2B27x-75=0\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "Notice we have a quadratic equation in the form of \"ax%5E2%2Bbx%2Bc\" where \"a=27\", \"b=27\", and \"c=-75\"\r
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\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for x\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\" Start with the quadratic formula\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-%2827%29+%2B-+sqrt%28+%2827%29%5E2-4%2827%29%28-75%29+%29%29%2F%282%2827%29%29\" Plug in \"a=27\", \"b=27\", and \"c=-75\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-27+%2B-+sqrt%28+729-4%2827%29%28-75%29+%29%29%2F%282%2827%29%29\" Square \"27\" to get \"729\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-27+%2B-+sqrt%28+729--8100+%29%29%2F%282%2827%29%29\" Multiply \"4%2827%29%28-75%29\" to get \"-8100\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-27+%2B-+sqrt%28+729%2B8100+%29%29%2F%282%2827%29%29\" Rewrite \"sqrt%28729--8100%29\" as \"sqrt%28729%2B8100%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-27+%2B-+sqrt%28+8829+%29%29%2F%282%2827%29%29\" Add \"729\" to \"8100\" to get \"8829\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-27+%2B-+sqrt%28+8829+%29%29%2F%2854%29\" Multiply \"2\" and \"27\" to get \"54\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-27+%2B-+9%2Asqrt%28109%29%29%2F%2854%29\" Simplify the square root (note: If you need help with simplifying square roots, check out this solver) \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-27%2B9%2Asqrt%28109%29%29%2F%2854%29\" or \"x+=+%28-27-9%2Asqrt%28109%29%29%2F%2854%29\" Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( "So the answers are \"x+=+%28-27%2B9%2Asqrt%28109%29%29%2F%2854%29\" or \"x+=+%28-27-9%2Asqrt%28109%29%29%2F%2854%29\" \r
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\n" ); document.write( "\n" ); document.write( "which approximate to \"x=1.24\" or \"x=-2.24\"
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