document.write( "Question 232291: 2x^4-15x^3+18x^2=0 Solve for x \n" ); document.write( "
Algebra.Com's Answer #171713 by eggsarecool(46)\"\" \"About 
You can put this solution on YOUR website!
Ok so first step is to factor out \"x%5E2\"\r
\n" ); document.write( "\n" ); document.write( "This would give you \"x%5E2%282x%5E2-15x%2B18%29=0\"\r
\n" ); document.write( "\n" ); document.write( "At this point you could factor the quadratic to become.\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2%283-2x%29%286-x%29=0\" At this point if one term becomes 0 the whole thing does since anything times 0 is 0.
\n" ); document.write( "Now solve \"+3-2x=0\" add 2x to both sides.
\n" ); document.write( "\"+2x=3+\" and now divide both sides by 2
\n" ); document.write( "\"x=3%2F2\" \r
\n" ); document.write( "\n" ); document.write( "For \"6-x=0\" add x to both sides
\n" ); document.write( "\"x=6\"
\n" ); document.write( "And for \"x%5E2=0\" take the square root of both sides
\n" ); document.write( "\"+sqrt%28x%5E2%29=sqrt%280%29\" since \"sqrt%28x%5E2%29=x\"
\n" ); document.write( "\"x=0\"\r
\n" ); document.write( "\n" ); document.write( "Your final answer for the problem would be \"x=+3%2F2%2C+6%2C+0\"\r
\n" ); document.write( "\n" ); document.write( "Now if you are not comfortable factoring the quadratic \"%282x%5E2-15x%2B18%29\"
\n" ); document.write( "You could use the quadratic formula instead \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "For the quadratic formula you take the numbers from \"%282x%5E2-15x%2B18%29\"
\n" ); document.write( "To give you \"+a=2\" \"b=-15\" \"c=18\"\r
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"2x%5E2%2B-15x%2B18+=+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=%28-15%29%5E2-4%2A2%2A18=81\".
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\n" ); document.write( " Discriminant d=81 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--15%2B-sqrt%28+81+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-15%29%2Bsqrt%28+81+%29%29%2F2%5C2+=+6\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-15%29-sqrt%28+81+%29%29%2F2%5C2+=+1.5\"
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\n" ); document.write( " Quadratic expression \"2x%5E2%2B-15x%2B18\" can be factored:
\n" ); document.write( " \"2x%5E2%2B-15x%2B18+=+2%28x-6%29%2A%28x-1.5%29\"
\n" ); document.write( " Again, the answer is: 6, 1.5.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-15%2Ax%2B18+%29\"

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\n" ); document.write( "\n" ); document.write( "And \"3%2F2=1.5\" it is just has just been converted to a decimal by the computer.
\n" ); document.write( "So you would get \"x=3%2F2\" \"x=1.5\" from the quadratic formula, and then you would still get \"x=0\" from \"x%5E2=0\". Same final answer, just two different methods.
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