document.write( "Question 85463: Hello, I've been trying to solve this equation but it seems I can only get down to simplifying it. Please help =)\r
\n" ); document.write( "\n" ); document.write( "SOLVE THE EQUATION SYMBOLICALLY\r
\n" ); document.write( "\n" ); document.write( "sqrt(x+6) + sqrt(2-x) = 4
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Algebra.Com's Answer #61688 by Earlsdon(6294)\"\" \"About 
You can put this solution on YOUR website!
Solve:
\n" ); document.write( "\"sqrt%28x%2B6%29+%2B+sqrt%282-x%29+=+4\" First, separate the square roots. Subtract \"sqrt%282-x%29\" from both sides.
\n" ); document.write( "\"sqrt%28x%2B6%29+=+4-sqrt%282-x%29\" Next, square both sides.
\n" ); document.write( "\"x%2B6+=+16-8%2Asqrt%282-x%29%2B%282-x%29\" Simplify so that you have only the radical \"sqrt%282-x%29\" (or a multiple thereof) on one side.
\n" ); document.write( "\"x%2B6+=+18-8%2Asqrt%282-x%29-x\" Add x to both sides.
\n" ); document.write( "\"2x%2B6+=+18-8%2Asqrt%282-x%29\" Subtract 18 from both sides.
\n" ); document.write( "\"2x-12+=+-8%2Asqrt%282-x%29\" Now square both sides again.
\n" ); document.write( "\"4x%5E2+-+48x+%2B+144+=+64%282-x%29\" Simplify this so that you have a quadratic equation in standard form.
\n" ); document.write( "\"4x%5E2+-+48x+%2B+144+=+128-64x\" Add 64x to both sides.
\n" ); document.write( "\"4x%5E2+%2B+16x+%2B144+=+128\" Subtract 128 from both sides.
\n" ); document.write( "\"4x%5E2+%2B+16x+%2B+16+=+0\" Factor out a 4 to simplify this.
\n" ); document.write( "\"4%28x%5E2+%2B+4x+%2B+4%29+=+0\" Now factor the parentheses.
\n" ); document.write( "\"%28x%2B2%29%28x%2B2%29+=+0\" Applying the zero products principle, you get the double root:
\n" ); document.write( "\"x+=+-2\"\r
\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "\"sqrt%28x%2B6%29+%2B+sqrt%282-x%29+=+4\" Set x = -2.
\n" ); document.write( "\"sqrt%28-2%2B6%29+%2B+sqrt%282-%28-2%29%29+=+4\" Simplify.
\n" ); document.write( "\"sqrt%284%29+%2B+sqrt%284%29+=+4\"
\n" ); document.write( "\"2+%2B+2+=+4\"
\n" ); document.write( "\"4+=+4\"
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