document.write( "Question 708291: |x − 11| = x2 − 11x \n" ); document.write( "
Algebra.Com's Answer #436063 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
\"abs%28x-11%29+=+x%5E2-11x\"
\n" ); document.write( "If this were
\n" ); document.write( "\"abs%28x-11%29+=+35\"
\n" ); document.write( "would it be easier? You probably know that this would be solved using two equations:
\n" ); document.write( "\"x-11+=+35\" or \"x-11+=+-35\"

\n" ); document.write( "Well, the problem we have can be solved in exactly the same way!
\n" ); document.write( "\"x-11+=+x%5E2-11x\" or \"x-11+=+-%28x%5E2-11x%29\"
\n" ); document.write( "The trick part is that we need the negative of the whole right side in the second equation. When the right side is just a number, like 35, you can just stick a \"-\" in front. But with multiple terms, like \"x%5E2-11x\", we need to put parentheses around the right side. With the parentheses, the \"-\" in front will negate the entire expression, not just the \"x%5E2\".

\n" ); document.write( "We now have two quadratic equations to solve. Let's do them one at a time. With the first equation we want one side to be zero. Subtracting the entire left side from both sides we get:
\n" ); document.write( "\"0+=+x%5E2-11x%2B11\"
\n" ); document.write( "This will not factor we we will use the Quadratic Formula:
\n" ); document.write( "\"x+=+%28-%28-11%29+%2B-+sqrt%28%28-11%29%5E2-4%281%29%2811%29%29%29%2F2%281%29\"
\n" ); document.write( "Simplifying...
\n" ); document.write( "\"x+=+%28-%28-11%29+%2B-+sqrt%28121-4%281%29%2811%29%29%29%2F2%281%29\"
\n" ); document.write( "\"x+=+%28-%28-11%29+%2B-+sqrt%28121-44%29%29%2F2%281%29\"
\n" ); document.write( "\"x+=+%28-%28-11%29+%2B-+sqrt%2877%29%29%2F2%281%29\"
\n" ); document.write( "\"x+=+%2811+%2B-+sqrt%2877%29%29%2F2\"
\n" ); document.write( "which is short for:
\n" ); document.write( "\"x+=+%2811+%2B+sqrt%2877%29%29%2F2\" or \"x+=+%2811+-+sqrt%2877%29%29%2F2\"

\n" ); document.write( "Now for the second equation we got earlier:
\n" ); document.write( "\"x-11+=+-%28x%5E2-11x%29\"
\n" ); document.write( "Before we get the zero, let's simplify the right side:
\n" ); document.write( "\"x-11+=+-x%5E2%2B11x%29\"
\n" ); document.write( "Adding \"x%5E2\" and subtracting 11x we get:
\n" ); document.write( "\"x%5E2-11x-11+=+0\"
\n" ); document.write( "Again this will not factor so again we use the formula:
\n" ); document.write( "\"x+=+%28-%28-11%29+%2B-+sqrt%28%28-11%29%5E2-4%281%29%28-11%29%29%29%2F2%281%29\"
\n" ); document.write( "Simplifying...
\n" ); document.write( "\"x+=+%28-%28-11%29+%2B-+sqrt%28121-4%281%29%28-11%29%29%29%2F2%281%29\"
\n" ); document.write( "\"x+=+%28-%28-11%29+%2B-+sqrt%28121%2B44%29%29%2F2%281%29\"
\n" ); document.write( "\"x+=+%28-%28-11%29+%2B-+sqrt%28165%29%29%2F2%281%29\"
\n" ); document.write( "\"x+=+%2811+%2B-+sqrt%28165%29%29%2F2\"
\n" ); document.write( "which is short for:
\n" ); document.write( "\"x+=+%2811+%2B+sqrt%28165%29%29%2F2\" or \"x+=+%2811+-+sqrt%28165%29%29%2F2\"

\n" ); document.write( "So there are four solutions to your equation:
\n" ); document.write( "\"x+=+%2811+%2B+sqrt%2877%29%29%2F2\" or \"x+=+%2811+-+sqrt%2877%29%29%2F2\"
\n" ); document.write( "\"x+=+%2811+%2B+sqrt%28165%29%29%2F2\" or \"x+=+%2811+-+sqrt%28165%29%29%2F2\" \n" ); document.write( "
\n" );