document.write( "Question 152795This question is from textbook Algebra 2 Texas
\n" ); document.write( ": Put $\"x=5y%5E2-25y%2B60\"$ in the form $\"x=a%28y-k%29%5E2%2Bh\"$ \n" ); document.write( "

Algebra.Com's Answer #112304 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( " $\"5y%5E2-25y%2B60\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"5%28y%5E2-5y%2B12%29\"$ Factor out the $\"y%5E2\"$ coefficient $\"5\"$ . This step is very important: the $\"y%5E2\"$ coefficient must be equal to 1.\r
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\n" ); document.write( "\n" ); document.write( "Take half of the $\"y\"$ coefficient $\"-5\"$ to get $\"-5%2F2\"$ . In other words, $\"%281%2F2%29%28-5%29=-5%2F2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now square $\"-5%2F2\"$ to get $\"25%2F4\"$ . In other words, $\"%28-5%2F2%29%5E2=%28-5%2F2%29%28-5%2F2%29=25%2F4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"5%28y%5E2-5y%2Bhighlight%2825%2F4-25%2F4%29%2B12%29\"$ Now add and subtract $\"25%2F4\"$ inside the parenthesis. Make sure to place this after the \"y\" term. Notice how $\"25%2F4-25%2F4=0\"$ . So the expression is not changed.\r
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\n" ); document.write( "\n" ); document.write( " $\"5%28%28y%5E2-5y%2B25%2F4%29-25%2F4%2B12%29\"$ Group the first three terms.\r
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\n" ); document.write( "\n" ); document.write( " $\"5%28%28y-5%2F2%29%5E2-25%2F4%2B12%29\"$ Factor $\"y%5E2-5y%2B25%2F4\"$ to get $\"%28y-5%2F2%29%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"5%28%28y-5%2F2%29%5E2%2B23%2F4%29\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( " $\"5%28y-5%2F2%29%5E2%2B5%2823%2F4%29\"$ Distribute.\r
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\n" ); document.write( "\n" ); document.write( " $\"5%28y-5%2F2%29%5E2%2B115%2F4\"$ Multiply.\r
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\n" ); document.write( "\n" ); document.write( "So after completing the square, $\"5y%5E2-25y%2B60\"$ transforms to $\"5%28y-5%2F2%29%5E2%2B115%2F4\"$ . So $\"5y%5E2-25y%2B60=5%28y-5%2F2%29%5E2%2B115%2F4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So $\"x=5y%5E2-25y%2B60\"$ is equivalent to $\"x=5%28y-5%2F2%29%5E2%2B115%2F4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "This means that the equation $\"x=5%28y-5%2F2%29%5E2%2B115%2F4\"$ is in the form $\"x=a%28y-k%29%5E2%2Bh\"$ where $\"a=5\"$ , $\"h=5%2F2\"$ , and $\"k=115%2F4\"$
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