document.write( "Question 213438: (x^2⁄2)- 4 – 6x = - 4\r
\n" ); document.write( "\n" ); document.write( "I need help with this . Can someone please explain what to do for me using this example. I need to know the steps as well as how you got the answer. Thankyou for you time. Your are appreshated. \n" ); document.write( "
Algebra.Com's Answer #161220 by drj(1380)\"\" \"About 
You can put this solution on YOUR website!
\"%28x%5E2%29%2F2-4%966x=-4+\"\r
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\n" ); document.write( "\n" ); document.write( "The following steps will simplify and solve the equation.\r
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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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  • This is an equation! Solutions: x=12,x=0.
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  • Graphical form: Equation \"%28x%5E2%29%2F2-4-6x=-4\" was fully solved.
  • Text form: (x^2)/2-4-6x=-4 simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+%28x%5E2%29%2F2-4-6x=-4+%29\"
    For tutors: simplify_cartoon( (x^2)/2-4-6x=-4 )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at \"highlight_red%28+%28highlight_red%28+x%5E2+%29%29%2F2+%29-4-6%2Ax=-4\".
Remove unneeded parentheses around factor \"highlight_red%28+x%5E2+%29\"
It becomes \"highlight_green%28+x%5E2+%29%2F2-4-6%2Ax=-4\".
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Look at \"x%5E2%2F2-highlight_red%28+4+%29-6%2Ax=-4\".
Moved \"-4\" to the right of expression
It becomes \"x%5E2%2F2-6%2Ax-highlight_green%28+4+%29=-4\".
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Look at \"x%5E2%2F2-6%2Ax-4=highlight_red%28+-4+%29\".
Moved these terms to the left \"highlight_green%28+4+%29\"
It becomes \"x%5E2%2F2-6%2Ax-4%2Bhighlight_green%28+4+%29=0\".
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Look at \"x%5E2%2F2-6%2Ax-highlight_red%28+4+%29%2Bhighlight_red%28+4+%29=0\".
Added fractions or integers together
It becomes \"x%5E2%2F2-6%2Ax%2Bhighlight_green%28+0+%29=0\".
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Look at \"x%5E2%2F2-6%2Ax%2Bhighlight_red%28+0+%29=0\".
Remove extraneous zero \"highlight_red%28+0+%29\"
It becomes \"x%5E2%2F2-6%2Ax=0\".
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Look at \"highlight_red%28+x%5E2%2F2-6%2Ax+%29=0\".
Equation \"highlight_red%28+x%5E2%2F2-6%2Ax=0+%29\" is a quadratic equation: 0.5*x^2-6*x =0, and has solutions 12,0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
\n" ); document.write( "This is an equation! Solutions: x=12,x=0.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "You can also use the quadratic formula given as\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"\r
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\n" ); document.write( "\n" ); document.write( "where a=1/2, b=-6, and c=0\r
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"0.5x%5E2%2B-6x%2B0+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-6%29%5E2-4%2A0.5%2A0=36\".
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\n" ); document.write( " Discriminant d=36 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--6%2B-sqrt%28+36+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+36+%29%29%2F2%5C0.5+=+12\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-6%29-sqrt%28+36+%29%29%2F2%5C0.5+=+0\"
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\n" ); document.write( " Quadratic expression \"0.5x%5E2%2B-6x%2B0\" can be factored:
\n" ); document.write( " \"0.5x%5E2%2B-6x%2B0+=+0.5%28x-12%29%2A%28x-0%29\"
\n" ); document.write( " Again, the answer is: 12, 0.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.5%2Ax%5E2%2B-6%2Ax%2B0+%29\"

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\n" ); document.write( "\n" ); document.write( "I hope the above steps were helpful.\r
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\n" ); document.write( "\n" ); document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r
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\n" ); document.write( "\n" ); document.write( "Good luck in your studies!\r
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\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J \n" ); document.write( "
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