document.write( "Question 110812: 1. Solve. (x + 4)^2 = 7
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Algebra.Com's Answer #80798 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
#1\r
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Start with the given equation\r
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Take the square root of both sides\r
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Subtract 4 from both sides to isolate x.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So our solution is:\r
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\r
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\n" ); document.write( "\n" ); document.write( "This means our solution breaks down to:\r
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\r
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\r
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\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B7x\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "Take half of the x coefficient 7 to get 3.5 (ie $\"7%2F2=3.5\"$ )\r
\n" ); document.write( "\n" ); document.write( "Now square 3.5 to get 12.25 (ie $\"%283.5%29%5E2=12.25\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B7x%2B12.25\"$ Add this result (12.25) to the expression. Now the expression $\"x%5E2%2B7x%2B12.25\"$ is a perfect square trinomial.\r
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\r
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\n" ); document.write( "\n" ); document.write( "#3\r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"y=-x%5E2%2B6x\"$ , we need to plot some points.\r
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\n" ); document.write( "\n" ); document.write( "We can start at any x value, so lets start at x=1\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%281%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-x%5E2%2B6x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-%281%29%5E2%2B6%281%29\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-1%2B6%281%29\"$ Evaluate $\"%281%29%5E2\"$ to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-1%2B6\"$ Multiply 6 and 1 to get 6\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=5\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , $\"f%28x%29=5\"$ \r
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\n" ); document.write( "\n" ); document.write( "-------Now lets find another point-------\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%282%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-x%5E2%2B6x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-%282%29%5E2%2B6%282%29\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-4%2B6%282%29\"$ Evaluate $\"-1%282%29%5E2\"$ to get -14\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-4%2B12\"$ Multiply 6 and 2 to get 12\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=8\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , $\"f%28x%29=8\"$ \r
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\n" ); document.write( "\n" ); document.write( "-------Now lets find another point-------\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%283%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-x%5E2%2B6x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-%283%29%5E2%2B6%283%29\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-9%2B6%283%29\"$ Evaluate $\"-1%283%29%5E2\"$ to get -19\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-9%2B18\"$ Multiply 6 and 3 to get 18\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=9\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , $\"f%28x%29=9\"$ \r
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\n" ); document.write( "\n" ); document.write( "-------Now lets find another point-------\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%284%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-x%5E2%2B6x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=-%284%29%5E2%2B6%284%29\"$ Plug in $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=-16%2B6%284%29\"$ Evaluate $\"-1%284%29%5E2\"$ to get -116\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=-16%2B24\"$ Multiply 6 and 4 to get 24\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=8\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ , $\"f%28x%29=8\"$ \r
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\n" ); document.write( "\n" ); document.write( "-------Now lets find another point-------\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%285%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-x%5E2%2B6x\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=-%285%29%5E2%2B6%285%29\"$ Plug in $\"x=5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=-25%2B6%285%29\"$ Evaluate $\"-1%285%29%5E2\"$ to get -125\r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=-25%2B30\"$ Multiply 6 and 5 to get 30\r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=5\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=5\"$ , $\"f%28x%29=5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now lets make a table of the values we have calculated\r
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document.write( " x y
 1 5
 2 8
 3 9
 4 8
 5 5\r\n" );
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Now plot the points\r
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\n" ); document.write( "\n" ); document.write( "Now connect the points to graph $\"y=-x%5E2%2B6x\"$ (note: the more points you plot, the easier it is to draw the graph)\r
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