document.write( "Question 164762: sqrt(26t+10)-5sqrt(t)=1 \n" ); document.write( "

Algebra.Com's Answer #121438 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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$\"sqrt%2826t%2B10%29+-+5sqrt%28t%29\"$ = 1
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\n" ); document.write( "Add $\"5sqrt%28t%29\"$ to both sides:
\n" ); document.write( " $\"sqrt%2826t%2B10%29\"$ = $\"1+%2B+5sqrt%28t%29\"$
\n" ); document.write( ":
\n" ); document.write( "Square both sides (FOIL the right side)
\n" ); document.write( "26t + 10 = 1 + $\"10sqrt%28t%29\"$ + 25t
\n" ); document.write( ":
\n" ); document.write( "Isolate the radical on the right
\n" ); document.write( "26t - 25t + 10 - 1 = $\"10sqrt%28t%29\"$
\n" ); document.write( ":
\n" ); document.write( "t + 9 = $\"10sqrt%28t%29\"$
\n" ); document.write( ":
\n" ); document.write( "Square both sides (FOIL the left)
\n" ); document.write( "t^2 + 18t + 81 = 100t
\n" ); document.write( ":
\n" ); document.write( "Arrange as a quadratic equation:
\n" ); document.write( "t^2 + 18t - 100t + 81 = 0
\n" ); document.write( ":
\n" ); document.write( "t^2 - 82t + 81 = 0
\n" ); document.write( "Factors to:
\n" ); document.write( "(t-81)(t-1) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "t = 81, and t = 1
\n" ); document.write( ":
\n" ); document.write( "Both solution should be checked in the original equation:
\n" ); document.write( "t=81
\n" ); document.write( " $\"sqrt%2826%2881%29%2B10%29+-+5sqrt%2881%29\"$ = 1
\n" ); document.write( " $\"sqrt%282106%2B10%29\"$ - 5 * 9 = 1
\n" ); document.write( " $\"sqrt%282116%29\"$ - 45 = 1
\n" ); document.write( "46 - 45 = 1; a good solution
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\n" ); document.write( "You can check x=1 solution \n" ); document.write( "

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