document.write( "Question 184184: Solve and show steps by completing the square:\r
\n" ); document.write( "\n" ); document.write( "x^2+8x+13=0 \n" ); document.write( "
Algebra.Com's Answer #138217 by jim_thompson5910(35256)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B8x%2B13\" Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( "Take half of the \"x\" coefficient \"8\" to get \"4\". In other words, \"%281%2F2%29%288%29=4\".\r
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\n" ); document.write( "\n" ); document.write( "Now square \"4\" to get \"16\". In other words, \"%284%29%5E2=%284%29%284%29=16\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B8x%2Bhighlight%2816-16%29%2B13\" Now add and subtract \"16\". Make sure to place this after the \"x\" term. Notice how \"16-16=0\". So the expression is not changed.\r
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\n" ); document.write( "\n" ); document.write( "\"%28x%5E2%2B8x%2B16%29-16%2B13\" Group the first three terms.\r
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\n" ); document.write( "\n" ); document.write( "\"%28x%2B4%29%5E2-16%2B13\" Factor \"x%5E2%2B8x%2B16\" to get \"%28x%2B4%29%5E2\".\r
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\n" ); document.write( "\n" ); document.write( "\"%28x%2B4%29%5E2-3\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So after completing the square, \"x%5E2%2B8x%2B13\" transforms to \"%28x%2B4%29%5E2-3\". So \"x%5E2%2B8x%2B13=%28x%2B4%29%5E2-3\".\r
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\n" ); document.write( "\n" ); document.write( "So \"x%5E2%2B8x%2B13=0\" is equivalent to \"%28x%2B4%29%5E2-3=0\".\r
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\n" ); document.write( "\n" ); document.write( "Now let's solve \"%28x%2B4%29%5E2-3=0\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28x%2B4%29%5E2-3=0\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"%28x%2B4%29%5E2=0%2B3\"Add \"3\" to both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"%28x%2B4%29%5E2=3\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "\"x%2B4=0%2B-sqrt%283%29\" Take the square root of both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"x%2B4=sqrt%283%29\" or \"x%2B4=-sqrt%283%29\" Break up the \"plus/minus\" to form two equations.\r
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\n" ); document.write( "\n" ); document.write( "\"x%2B4=sqrt%283%29\" or \"x%2B4=-sqrt%283%29\" Simplify the square root.\r
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\n" ); document.write( "\n" ); document.write( "\"x=-4%2Bsqrt%283%29\" or \"x=-4-sqrt%283%29\" Subtract \"4\" from 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=-4%2Bsqrt%283%29\" or \"x=-4-sqrt%283%29\".
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