document.write( "Question 248346: Here are three questions I need help with:\r
\n" ); document.write( "\n" ); document.write( "1.) 5d^2 - 10d = 0 (factoring problem)\r
\n" ); document.write( "\n" ); document.write( "2.) 8x^2 = 16 (factoring problem)\r
\n" ); document.write( "\n" ); document.write( "3.) 3m^2 - 5m = -2 (factoring problem)\r
\n" ); document.write( "\n" ); document.write( "And my teacher only likes the answers in fractions or radicals, no decimals.
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Algebra.Com's Answer #180980 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "\"5d%5E2-10d=0\" Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "\"5d%28d-2%29=0\" Factor out the GCF 5d.\r
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\n" ); document.write( "\n" ); document.write( "Now set each factor equal to zero:\r
\n" ); document.write( "\n" ); document.write( "\"5d=0\" or \"d-2=0\" \r
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\n" ); document.write( "\n" ); document.write( "\"d=0\" or \"d=2\" Solve for d in each case\r
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\n" ); document.write( "\n" ); document.write( "So our answers are \r
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\n" ); document.write( "\n" ); document.write( " \"d=0\" or \"d=2\"\r
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\n" ); document.write( "\n" ); document.write( "\"8x%5E2+=+16\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"8x%5E2+-+16=0\" Subtract 16 from both sides.\r
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\n" ); document.write( "\n" ); document.write( "Notice that the quadratic \"8x%5E2-16\" is in the form of \"Ax%5E2%2BBx%2BC\" where \"A=8\", \"B=0\", and \"C=-16\"\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-%280%29+%2B-+sqrt%28+%280%29%5E2-4%288%29%28-16%29+%29%29%2F%282%288%29%29\" Plug in \"A=8\", \"B=0\", and \"C=-16\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-0+%2B-+sqrt%28+0-4%288%29%28-16%29+%29%29%2F%282%288%29%29\" Square \"0\" to get \"0\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-0+%2B-+sqrt%28+0--512+%29%29%2F%282%288%29%29\" Multiply \"4%288%29%28-16%29\" to get \"-512\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-0+%2B-+sqrt%28+0%2B512+%29%29%2F%282%288%29%29\" Rewrite \"sqrt%280--512%29\" as \"sqrt%280%2B512%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-0+%2B-+sqrt%28+512+%29%29%2F%282%288%29%29\" Add \"0\" to \"512\" to get \"512\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-0+%2B-+sqrt%28+512+%29%29%2F%2816%29\" Multiply \"2\" and \"8\" to get \"16\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-0+%2B-+16%2Asqrt%282%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+=+%28-0%29%2F%2816%29+%2B-+%2816%2Asqrt%282%29%29%2F%2816%29\" Break up the fraction. \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+0+%2B-+sqrt%282%29\" Reduce. \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+sqrt%282%29\" or \"x+=+-sqrt%282%29\" Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( "So the solutions are \"x+=+sqrt%282%29\" or \"x+=+-sqrt%282%29\" \r
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\n" ); document.write( "\n" ); document.write( "\"3m%5E2-5m=-2\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"3m%5E2-5m%2B2=0\" Add 2 to both sides.\r
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\n" ); document.write( "\n" ); document.write( "Notice that the quadratic \"3m%5E2-5m%2B2\" is in the form of \"Am%5E2%2BBm%2BC\" where \"A=3\", \"B=-5\", and \"C=2\"\r
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\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for \"m\":\r
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\n" ); document.write( "\n" ); document.write( "\"m+=+%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( "\"m+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%283%29%282%29+%29%29%2F%282%283%29%29\" Plug in \"A=3\", \"B=-5\", and \"C=2\"\r
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\n" ); document.write( "\n" ); document.write( "\"m+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%283%29%282%29+%29%29%2F%282%283%29%29\" Negate \"-5\" to get \"5\". \r
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\n" ); document.write( "\n" ); document.write( "\"m+=+%285+%2B-+sqrt%28+25-4%283%29%282%29+%29%29%2F%282%283%29%29\" Square \"-5\" to get \"25\". \r
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\n" ); document.write( "\n" ); document.write( "\"m+=+%285+%2B-+sqrt%28+25-24+%29%29%2F%282%283%29%29\" Multiply \"4%283%29%282%29\" to get \"24\"\r
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\n" ); document.write( "\n" ); document.write( "\"m+=+%285+%2B-+sqrt%28+1+%29%29%2F%282%283%29%29\" Subtract \"24\" from \"25\" to get \"1\"\r
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\n" ); document.write( "\n" ); document.write( "\"m+=+%285+%2B-+sqrt%28+1+%29%29%2F%286%29\" Multiply \"2\" and \"3\" to get \"6\". \r
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\n" ); document.write( "\n" ); document.write( "\"m+=+%285+%2B-+1%29%2F%286%29\" Take the square root of \"1\" to get \"1\". \r
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\n" ); document.write( "\n" ); document.write( "\"m+=+%285+%2B+1%29%2F%286%29\" or \"m+=+%285+-+1%29%2F%286%29\" Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( "\"m+=+%286%29%2F%286%29\" or \"m+=++%284%29%2F%286%29\" Combine like terms. \r
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\n" ); document.write( "\n" ); document.write( "\"m+=+1\" or \"m+=+2%2F3\" Simplify. \r
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\n" ); document.write( "\n" ); document.write( "So the solutions are \"m+=+1\" or \"m+=+2%2F3\" \r
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