document.write( "Question 322154: Find all solutions. x^2 + x - 2 + square root of (x^2 + x) = 0 \n" ); document.write( "

Algebra.Com's Answer #230653 by Jk22(389) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x%5E2+%2B+x+-+2+%2B+sqrt%28x%5E2+%2B+x%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( "= $\"%28x%2B2%29%28x-1%29%2Bsqrt%28x%28x%2B1%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "=> $\"%28x%2B2%29%28x-1%29=-sqrt%28x%28x%2B1%29%29\"$ --->domains : x in [-2;1]^]-1;0[=[-2;-1]U[0;1]\r
\n" ); document.write( "\n" ); document.write( "symmetry : let x=y-1/2 :\r
\n" ); document.write( "\n" ); document.write( " $\"%28y%2B3%2F2%29%28y-3%2F2%29=-sqrt%28%28y-1%2F2%29%28y%2B1%2F2%29%29\"$ | square\r
\n" ); document.write( "\n" ); document.write( " $\"%28y%5E2-9%2F4%29%5E2=%28y%5E2-1%2F4%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y%5E4-%289%2F2%29%2Ay%5E2%2B81%2F16=y%5E2-1%2F4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y%5E4-%2811%2F2%29%2Ay%5E2%2B85%2F16=0\"$ \r
\n" ); document.write( "\n" ); document.write( "=> y^2=(11+-6)/4=17/4 or 5/4\r
\n" ); document.write( "\n" ); document.write( "solution in domain : $\"x=%28%2B-+sqrt%285%29-1%29%2F2\"$ \n" ); document.write( "

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