document.write( "Question 969578: x^2-2x+sqrt(x^2-2x-2)=4 \n" ); document.write( "

Algebra.Com's Answer #592416 by josgarithmetic(39617) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x%5E2-2x%2Bsqrt%28x%5E2-2x-2%29=4\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You need to isolate the irrational expression.
\n" ); document.write( " $\"sqrt%28x%5E2-2x-2%29=-x%5E2%2B2x%2B4\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Square both sides.
\n" ); document.write( " $\"x%5E2-2x-2=%28-x%5E2%2B2x%2B4%29%5E2\"$
\n" ); document.write( " $\"x%5E2-2x-2=x%5E4-4x%5E3-4x%5E2%2B16x%2B16\"$
\n" ); document.write( " $\"highlight_green%28x%5E4-4x%5E3-5x%5E2%2B18x%2B18=0%29\"$ -----You could take the rest of the process. You want to try looking for Rational Roots to try to factorize the polynomial. (Rational Roots Theorem). Several possible roots to test for:
\n" ); document.write( "The plusses and minuses of 1,2,3,6,9; and there might be complex roots - not know until you try.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Roots Found Through Synthetic Division:
\n" ); document.write( "-1, 3,
\n" ); document.write( "Resulting coefficients after that give $\"x%5E2-2x-6\"$ discriminant of 28, so two more IRRATIONAL roots. General solution to quadratic equation will give -1-sqrt(7) and -1+sqrt(7).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----------------------------------------------------
\n" ); document.write( "Solution Set:
\n" ); document.write( "-1, 3, $\"-1-sqrt%287%29\"$ , and $\"-1%2Bsqrt%287%29\"$ .
\n" ); document.write( "----------------------------------------------------- \n" ); document.write( "

\n" );