document.write( "Question 475331: Please help me find the roots of:\r
\n" ); document.write( "\n" ); document.write( " $\"sqrt%28sqrt%28x%2B5%29%2Bx%29=5\"$ \n" ); document.write( "

Algebra.Com's Answer #326102 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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$\"sqrt%28sqrt%28x%2B5%29%2Bx%29=5\"$
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\n" ); document.write( "Square both sides
\n" ); document.write( " $\"sqrt%28x%2B5%29%2Bx=25\"$
\n" ); document.write( ":
\n" ); document.write( "subtract x from both sides
\n" ); document.write( " $\"sqrt%28x%2B5%29=25-x\"$
\n" ); document.write( ":
\n" ); document.write( "Square both sides again
\n" ); document.write( "x + 5 = (25-x)^2
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\n" ); document.write( "FOIL (25-x)(25-x)
\n" ); document.write( "x + 5 = 625 - 50x + x^2
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\n" ); document.write( "Combine as a quadratic equation
\n" ); document.write( "x^2 - 50x - x + 625 - 5 = 0
\n" ); document.write( "x^2 - 51x + 620 = 0
\n" ); document.write( "You can use the quadratic formula to solve this; a=1, b=-51,c=620, but
\n" ); document.write( "this will factor to:
\n" ); document.write( "(x-20)(x-31) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "x = 20
\n" ); document.write( "x = 31
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\n" ); document.write( ":
\n" ); document.write( "Try both solutions in the original equation, only x=20 will work \n" ); document.write( "

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