document.write( "Question 260559: Could you help solve the quadratic equatin by completing the square
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\n" ); document.write( "Stacie Rihl
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Algebra.Com's Answer #191921 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "\"2x%5E2-6x%2B5\" Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( "\"2%28x%5E2-3x%2B5%2F2%29\" Factor out the \"x%5E2\" coefficient \"2\". This step is very important: the \"x%5E2\" coefficient must be equal to 1.\r
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\n" ); document.write( "\n" ); document.write( "Take half of the \"x\" coefficient \"-3\" to get \"-3%2F2\". In other words, \"%281%2F2%29%28-3%29=-3%2F2\".\r
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\n" ); document.write( "\n" ); document.write( "Now square \"-3%2F2\" to get \"9%2F4\". In other words, \"%28-3%2F2%29%5E2=%28-3%2F2%29%28-3%2F2%29=9%2F4\"\r
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\n" ); document.write( "\n" ); document.write( "\"2%28x%5E2-3x%2Bhighlight%289%2F4-9%2F4%29%2B5%2F2%29\" Now add and subtract \"9%2F4\" inside the parenthesis. Make sure to place this after the \"x\" term. Notice how \"9%2F4-9%2F4=0\". So the expression is not changed.\r
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\n" ); document.write( "\n" ); document.write( "\"2%28%28x%5E2-3x%2B9%2F4%29-9%2F4%2B5%2F2%29\" Group the first three terms.\r
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\n" ); document.write( "\n" ); document.write( "\"2%28%28x-3%2F2%29%5E2-9%2F4%2B5%2F2%29\" Factor \"x%5E2-3x%2B9%2F4\" to get \"%28x-3%2F2%29%5E2\".\r
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\n" ); document.write( "\n" ); document.write( "\"2%28%28x-3%2F2%29%5E2%2B1%2F4%29\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "\"2%28x-3%2F2%29%5E2%2B2%281%2F4%29\" Distribute.\r
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\n" ); document.write( "\n" ); document.write( "\"2%28x-3%2F2%29%5E2%2B1%2F2\" Multiply.\r
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\n" ); document.write( "\n" ); document.write( "So after completing the square, \"2x%5E2-6x%2B5\" transforms to \"2%28x-3%2F2%29%5E2%2B1%2F2\". So \"2x%5E2-6x%2B5=2%28x-3%2F2%29%5E2%2B1%2F2\".\r
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\n" ); document.write( "\n" ); document.write( "So \"2x%5E2-6x%2B5=0\" is equivalent to \"2%28x-3%2F2%29%5E2%2B1%2F2=0\".\r
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\n" ); document.write( "\n" ); document.write( "Now let's solve \"2%28x-3%2F2%29%5E2%2B1%2F2=0\" \r
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\n" ); document.write( "\n" ); document.write( "\"2%28x-3%2F2%29%5E2%2B1%2F2=0\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"2%28x-3%2F2%29%5E2=0-1%2F2\" Subtract \"1%2F2\" from both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"2%28x-3%2F2%29%5E2=-1%2F2\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-3%2F2%29%5E2=%28-1%2F2%29%2F%282%29\" Divide both sides by \"2\".\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-3%2F2%29%5E2=-1%2F4\" Reduce.\r
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\n" ); document.write( "\n" ); document.write( "\"x-3%2F2=%22%22%2B-sqrt%28-1%2F4%29\" Take the square root of both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"x-3%2F2=sqrt%28-1%2F4%29\" or \"x-3%2F2=-sqrt%28-1%2F4%29\" Break up the \"plus/minus\" to form two equations.\r
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\n" ); document.write( "\n" ); document.write( "\"x-3%2F2=%281%2F2%29i\" or \"x-3%2F2=-%281%2F2%29i\" Take the square root of \"-1%2F4\" to get \"%281%2F2%29i\".\r
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\n" ); document.write( "\n" ); document.write( "Note: \"i=sqrt%28-1%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x=3%2F2%2B%281%2F2%29i\" or \"x=3%2F2-%281%2F2%29i\" Add \"3%2F2\" to both sides.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So the solutions are \"x=3%2F2%2B%281%2F2%29i\" or \"x=3%2F2-%281%2F2%29i\".\r
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