document.write( "Question 49091: May you please help me with this? 4x² - 8x = 5 \n" ); document.write( "
Algebra.Com's Answer #32541 by AnlytcPhil(1806)\"\" \"About 
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May you please help me with this?\r\n" );
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document.write( "        4x² — 8x = 5\r\n" );
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document.write( "Get 0 on the right by adding -5 to both sides\r\n" );
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document.write( "    4x² — 8x — 5 = 0\r\n" );
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document.write( "Now we factor the left side\r\n" );
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document.write( "    4x² — 8x — 5 = 0\r\n" );
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document.write( "4x² — 8x — 5 = 0\r\n" );
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document.write( "Multiply the red 4 by the blue 5, which gives\r\n" );
document.write( "20, Now since the green sign is \" — \", we \r\n" );
document.write( "think of two integers which have product equal\r\n" );
document.write( "to 20 and which have difference equal to the \r\n" );
document.write( "purple 8.\r\n" );
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document.write( "Such integers are 10 and 2. So we use these to\r\n" );
document.write( "rewrite the -8x as -10x + 2x\r\n" );
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document.write( "4x² - 10x + 2x - 5 = 0\r\n" );
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document.write( "Now we factor 2x out of the first two terms\r\n" );
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document.write( "2x(2x - 5) + 2x - 5 = 0\r\n" );
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document.write( "Now we factor 1 out of the last two terms:\r\n" );
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document.write( "2x(2x - 5) + 1(2x - 5) = 0\r\n" );
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document.write( "Notice there is a common factor of (2x - 5)\r\n" );
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document.write( "So take out the common\r\n" );
document.write( "factor (2x - 5) and put the factors 2x and +1\r\n" );
document.write( "inside parentheses on the right:\r\n" );
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document.write( "(2x - 5)(2x + 1) = 0\r\n" );
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document.write( "Now we set each factor in parentheses equal to\r\n" );
document.write( "0 and solve\r\n" );
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document.write( "Setting 2x - 5 = 0\r\n" );
document.write( "            2x = 5\r\n" );
document.write( "             x = 5/2\r\n" );
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document.write( "Setting 2x + 1 = 0\r\n" );
document.write( "            2x = -1\r\n" );
document.write( "             x = -1/2 \r\n" );
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document.write( "So the two solutions are 5/2 and -1/2\r\n" );
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document.write( "Edwin
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