document.write( "Question 357118: Solving Quadraticc Equations by Completing the Square\r
\n" ); document.write( "\n" ); document.write( "2x^2 - x + 6 = 0\r
\n" ); document.write( "\n" ); document.write( "Thank you for your time and help. \n" ); document.write( "
Algebra.Com's Answer #255026 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"2x%5E2-x%2B6\" Start with the given expression.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2%28x%5E2-%281%2F2%29x%2B3%29\" Factor out the \"x%5E2\" coefficient \"2\". This step is very important: the \"x%5E2\" coefficient must be equal to 1.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Take half of the \"x\" coefficient \"-1%2F2\" to get \"-1%2F4\". In other words, \"%281%2F2%29%28-1%2F2%29=-1%2F4\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now square \"-1%2F4\" to get \"1%2F16\". In other words, \"%28-1%2F4%29%5E2=%28-1%2F4%29%28-1%2F4%29=1%2F16\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2%28x%5E2-%281%2F2%29x%2Bhighlight%281%2F16-1%2F16%29%2B3%29\" Now add and subtract \"1%2F16\" inside the parenthesis. Make sure to place this after the \"x\" term. Notice how \"1%2F16-1%2F16=0\". So the expression is not changed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2%28%28x%5E2-%281%2F2%29x%2B1%2F16%29-1%2F16%2B3%29\" Group the first three terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2%28%28x-1%2F4%29%5E2-1%2F16%2B3%29\" Factor \"x%5E2-%281%2F2%29x%2B1%2F16\" to get \"%28x-1%2F4%29%5E2\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2%28%28x-1%2F4%29%5E2%2B47%2F16%29\" Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2%28x-1%2F4%29%5E2%2B2%2847%2F16%29\" Distribute.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2%28x-1%2F4%29%5E2%2B47%2F8\" Multiply.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So after completing the square, \"2x%5E2-x%2B6\" transforms to \"2%28x-1%2F4%29%5E2%2B47%2F8\". So \"2x%5E2-x%2B6=2%28x-1%2F4%29%5E2%2B47%2F8\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So \"2x%5E2-x%2B6=0\" is equivalent to \"2%28x-1%2F4%29%5E2%2B47%2F8=0\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's solve \"2%28x-1%2F4%29%5E2%2B47%2F8=0\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2%28x-1%2F4%29%5E2%2B47%2F8=0\" Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2%28x-1%2F4%29%5E2=0-47%2F8\"Subtract \"47%2F8\" from both sides.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2%28x-1%2F4%29%5E2=-47%2F8\" Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%28x-1%2F4%29%5E2=%28-47%2F8%29%2F%282%29\" Divide both sides by \"2\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%28x-1%2F4%29%5E2=-47%2F16\" Reduce.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x-1%2F4=%22%22%2B-sqrt%28-47%2F16%29\" Take the square root of both sides.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x-1%2F4=sqrt%28-47%2F16%29\" or \"x-1%2F4=-sqrt%28-47%2F16%29\" Break up the \"plus/minus\" to form two equations.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x-1%2F4=i%2A%28sqrt%2847%29%29%2F4%29\" or \"x-1%2F4=-i%2A%28sqrt%2847%29%29%2F4%29\" Simplify the square root.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x=1%2F4%2Bi%2A%28sqrt%2847%29%29%2F4%29\" or \"x=1%2F4-i%2A%28sqrt%2847%29%29%2F4%29\" Add \"1%2F4\" to both sides.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x=%281%2Bi%2Asqrt%2847%29%29%2F4\" or \"x=%281-i%2Asqrt%2847%29%29%2F4\" Combine the fractions.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "--------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Answer:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the solutions are \"x=%281%2Bi%2Asqrt%2847%29%29%2F4\" or \"x=%281-i%2Asqrt%2847%29%29%2F4\" where \"i=sqrt%28-1%29\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also, feel free to check out my tutoring website\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Jim \n" ); document.write( "
\n" );