document.write( "Question 132426: Solve.\r
\n" ); document.write( "\n" ); document.write( "6x^4-19x^2+10=0\r
\n" ); document.write( "\n" ); document.write( "I tried using the solver and the answer didn't look right to me. Can you show me how to solve so I can understand the steps. \n" ); document.write( "
Algebra.Com's Answer #96763 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
Which solver did you use? \r
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\n" ); document.write( "\n" ); document.write( "\"6x%5E4-19x%5E2%2B10=0+\" Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "Let \"u=x%5E2\"\r
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\n" ); document.write( "\n" ); document.write( "\"6u%5E2-19u%2B10=0+\" Plug in \"u=x%5E2\"\r
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Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for u:

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\n" ); document.write( " Starting with the general quadratic
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\n" ); document.write( " \"au%5E2%2Bbu%2Bc=0\"
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\n" ); document.write( " the general solution using the quadratic equation is:
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\n" ); document.write( " \"u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"
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\n" ); document.write( " So lets solve \"6%2Au%5E2-19%2Au%2B10=0\" ( notice \"a=6\", \"b=-19\", and \"c=10\")
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\n" ); document.write( " \"u+=+%28--19+%2B-+sqrt%28+%28-19%29%5E2-4%2A6%2A10+%29%29%2F%282%2A6%29\" Plug in a=6, b=-19, and c=10
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\n" ); document.write( " \"u+=+%2819+%2B-+sqrt%28+%28-19%29%5E2-4%2A6%2A10+%29%29%2F%282%2A6%29\" Negate -19 to get 19
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\n" ); document.write( " \"u+=+%2819+%2B-+sqrt%28+361-4%2A6%2A10+%29%29%2F%282%2A6%29\" Square -19 to get 361 (note: remember when you square -19, you must square the negative as well. This is because \"%28-19%29%5E2=-19%2A-19=361\".)
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\n" ); document.write( " \"u+=+%2819+%2B-+sqrt%28+361%2B-240+%29%29%2F%282%2A6%29\" Multiply \"-4%2A10%2A6\" to get \"-240\"
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\n" ); document.write( " \"u+=+%2819+%2B-+sqrt%28+121+%29%29%2F%282%2A6%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"u+=+%2819+%2B-+11%29%2F%282%2A6%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
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\n" ); document.write( " \"u+=+%2819+%2B-+11%29%2F12\" Multiply 2 and 6 to get 12
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( " \"u+=+%2819+%2B+11%29%2F12\" or \"u+=+%2819+-+11%29%2F12\"
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\n" ); document.write( " Lets look at the first part:
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\n" ); document.write( " \"x=%2819+%2B+11%29%2F12\"
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\n" ); document.write( " \"u=30%2F12\" Add the terms in the numerator
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\n" ); document.write( " \"u=5%2F2\" Divide
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\n" ); document.write( " So one answer is
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\n" ); document.write( " \"u=5%2F2\"
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\n" ); document.write( " Now lets look at the second part:
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\n" ); document.write( " \"x=%2819+-+11%29%2F12\"
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\n" ); document.write( " \"u=8%2F12\" Subtract the terms in the numerator
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\n" ); document.write( " \"u=2%2F3\" Divide
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\n" ); document.write( " So another answer is
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\n" ); document.write( " \"u=2%2F3\"
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\n" ); document.write( " So our solutions are:
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\n" ); document.write( " \"u=5%2F2\" or \"u=2%2F3\"
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\n" ); document.write( "\n" ); document.write( "Remember, we let \"u=x%5E2\". So this means that \r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2=5%2F2\" or \"x%5E2=2%2F3\"\r
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\n" ); document.write( "\n" ); document.write( "\"x=0%2B-sqrt%285%2F2%29\" or \"x=0%2B-sqrt%282%2F3%29\" Take the square root of both sides for each case\r
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\n" ); document.write( "\n" ); document.write( "Break up the two expressions\r
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\n" ); document.write( "\n" ); document.write( "\"x=sqrt%285%2F2%29\", \"x=-sqrt%285%2F2%29\", \"x=sqrt%282%2F3%29\" or \"x=-sqrt%282%2F3%29\" \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So our solutions are\r
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\n" ); document.write( "\n" ); document.write( "\"x=sqrt%285%2F2%29\", \"x=-sqrt%285%2F2%29\", \"x=sqrt%282%2F3%29\" or \"x=-sqrt%282%2F3%29\" \n" ); document.write( "
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