document.write( "Question 30525: please help! I'm getting stuck in the middle of this problem. I know to separate the radicals square both sides, then isolate radical but I am not coming up with the correct answer. Any help is appreciated!
\n" ); document.write( "Thanks
\n" ); document.write( "Jane P.\r
\n" ); document.write( "\n" ); document.write( "sqrt(2x+5) + sqrt(x+6) = 9 \n" ); document.write( "
Algebra.Com's Answer #17156 by sdmmadam@yahoo.com(530)\"\" \"About 
You can put this solution on YOUR website!
sqrt(2x+5) + sqrt(x+6) = 9----(1)
\n" ); document.write( "sqrt(2x+5) = 9 - sqrt(x+6)
\n" ); document.write( "Squaring both the sides
\n" ); document.write( "[sqrt(2x+5)]^2 = [9 - sqrt(x+6)]^2
\n" ); document.write( "(2x+5) = 9^2+(x+6)-2X9X sqrt(x+6)
\n" ); document.write( "[using [sqrt(p)]^2 = p on the LHS (as well as later in the RHS
\n" ); document.write( "and formula: (a-b)^2 = a^2+b^2-2ab where here a=9,b = sqrt(x+6)]
\n" ); document.write( "2x+5 = 81+x+6-18sqrt(x+6)
\n" ); document.write( "(2x-x)+(5-81-6) = -18sqrt(x+6)
\n" ); document.write( "(x-82) = -18sqrt(x+6)
\n" ); document.write( "Squaring both the sides
\n" ); document.write( "(x-82)^2 = [-18sqrt(x+6)]^2
\n" ); document.write( "x^2-164x+6724 = 324(x+6)
\n" ); document.write( "x^2-164x+6724 = 324x +1944
\n" ); document.write( "x^2-164x-324x+6724-1944 =0
\n" ); document.write( "x^2-488x+4780 =0
\n" ); document.write( "(sum is -488 and productis +4780 and therefore the quantiies are(-478)and (-10))
\n" ); document.write( "x^2-10x-478x-4780 = 0
\n" ); document.write( "x(x-10)-478(x-10) = 0
\n" ); document.write( "xp-478p = 0 where p = (x-10)
\n" ); document.write( "p(x-478) = 0
\n" ); document.write( "(x-10)(x-478) =0 (putting p back)
\n" ); document.write( "(x-10) = 0 gives x = 10
\n" ); document.write( "(x-478) = 0 gives x = 478
\n" ); document.write( "Answer: x = 10 and x = 478
\n" ); document.write( "Verification: x = 10 in (1)
\n" ); document.write( "LHS=sqrt(2x+5) + sqrt(x+6)
\n" ); document.write( "=sqrt[(2X10+5)] + sqrt[(10+6)]
\n" ); document.write( "= sqrt[(25)] + sqrt[(16)]
\n" ); document.write( "=5+4
\n" ); document.write( "=9
\n" ); document.write( "=RHS
\n" ); document.write( "Regarding the other huge number looking at the small number 9 on the RHS tells us that at least one of the roots we should take negative to comply with the answer:
\n" ); document.write( "x = 10 in (1)
\n" ); document.write( "LHS=sqrt(2x+5) + sqrt(x+6)
\n" ); document.write( "=sqrt[(2X478+5)] + sqrt[(478+6)]
\n" ); document.write( "= sqrt[(961)] + sqrt[(484)]
\n" ); document.write( "= 31-22
\n" ); document.write( "=9
\n" ); document.write( "=RHS\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );