document.write( "Question 139847: square root of (x-5) - square root of (2x+7) = -3 \n" ); document.write( "

Algebra.Com's Answer #101957 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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square root of (x-5) - square root of (2x+7) = -3
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\n" ); document.write( " $\"sqrt%28x-5%29\"$ - $\"sqrt%282x%2B7%29\"$ = -3
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\n" ); document.write( "We can arrange this to get rid of the negatives and make it a little easier
\n" ); document.write( " $\"sqrt%28x-5%29\"$ + 3 = $\"sqrt%282x%2B7%29\"$
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\n" ); document.write( "Square both sides (FOIL the left side)
\n" ); document.write( "[(x-5) + $\"6sqrt%28x-5%29\"$ + 9] = 2x + 7
\n" ); document.write( ":
\n" ); document.write( "x + $\"6sqrt%28x-5%29\"$ + 9 - 5 = 2x + 7
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\n" ); document.write( "x + $\"6sqrt%28x-5%29\"$ + 4 = 2x + 7
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\n" ); document.write( "We want the radical by itself on the left:
\n" ); document.write( " $\"6sqrt%28x-5%29\"$ = 2x -x + 7 - 4
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\n" ); document.write( " $\"6sqrt%28x-5%29\"$ = (x + 3)
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\n" ); document.write( "Square both sides again (FOIL the right side)
\n" ); document.write( "36(x-5) = x^2 + 6x + 9
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\n" ); document.write( "36x - 180 = x^2 + 6x + 9
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\n" ); document.write( "combine like terms to obtain a quadratic equation
\n" ); document.write( "0 = x^2 + 6x - 36x + 9 + 180
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\n" ); document.write( "x^2 - 30x + 189 = 0
\n" ); document.write( "Factor
\n" ); document.write( "(x-9)(x-21) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "x = 9
\n" ); document.write( "x = 21
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\n" ); document.write( "Try both solutions in the original equation to make sure they are both valid\r
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