document.write( "Question 38943: Solve using the quadratic formula
\n" ); document.write( "\"3x%5E2-14x=-15\"\r
\n" ); document.write( "\n" ); document.write( "\"5x%5E2=x%2B2\"\r
\n" ); document.write( "\n" ); document.write( "\"4x%5E2=12x-9\"\r
\n" ); document.write( "\n" ); document.write( "I need help on these also it looks like this on the paper\r
\n" ); document.write( "\n" ); document.write( "Solve. Express irrational solutions in simplest radical form.\r
\n" ); document.write( "\n" ); document.write( "\"2x%5E2=128\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B25=0\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2=25%2F36\"\r
\n" ); document.write( "\n" ); document.write( "\"0=6x%5E2-24\"\r
\n" ); document.write( "\n" ); document.write( "\"2%28x%2B3%29%5E2-4=68\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B5x-24=0\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2-3x-28=0\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2-49=0\"\r
\n" ); document.write( "\n" ); document.write( "\"5x%5E2-2x-7=0\"\r
\n" ); document.write( "\n" ); document.write( "\"+sqrt+%283x=9%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"+sqrt+%28x%2B2-7=2%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"+sqrt+%28x-4-9=4%29+\"\r
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Algebra.Com's Answer #24427 by Nate(3500)\"\" \"About 
You can put this solution on YOUR website!
\"3x%5E2-14x%2B15=0\"
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"3x%5E2%2B-14x%2B15+=+0\") has the following solutons:
\n" ); document.write( "
\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.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-14%29%5E2-4%2A3%2A15=16\".
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\n" ); document.write( " Discriminant d=16 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--14%2B-sqrt%28+16+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-14%29%2Bsqrt%28+16+%29%29%2F2%5C3+=+3\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-14%29-sqrt%28+16+%29%29%2F2%5C3+=+1.66666666666667\"
\n" ); document.write( "
\n" ); document.write( " Quadratic expression \"3x%5E2%2B-14x%2B15\" can be factored:
\n" ); document.write( " \"3x%5E2%2B-14x%2B15+=+3%28x-3%29%2A%28x-1.66666666666667%29\"
\n" ); document.write( " Again, the answer is: 3, 1.66666666666667.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-14%2Ax%2B15+%29\"

\n" ); document.write( "\n" ); document.write( ".
\n" ); document.write( "\"5x%5E2-x-2=0\"
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"5x%5E2%2B-1x%2B-2+=+0\") has the following solutons:
\n" ); document.write( "
\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=%28-1%29%5E2-4%2A5%2A-2=41\".
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\n" ); document.write( " Discriminant d=41 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--1%2B-sqrt%28+41+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+41+%29%29%2F2%5C5+=+0.740312423743285\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-1%29-sqrt%28+41+%29%29%2F2%5C5+=+-0.540312423743285\"
\n" ); document.write( "
\n" ); document.write( " Quadratic expression \"5x%5E2%2B-1x%2B-2\" can be factored:
\n" ); document.write( " \"5x%5E2%2B-1x%2B-2+=+5%28x-0.740312423743285%29%2A%28x--0.540312423743285%29\"
\n" ); document.write( " Again, the answer is: 0.740312423743285, -0.540312423743285.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-1%2Ax%2B-2+%29\"

\n" ); document.write( "\n" ); document.write( ".
\n" ); document.write( "\"4x%5E2-12x%2B9=0\"
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"4x%5E2%2B-12x%2B9+=+0\") has the following solutons:
\n" ); document.write( "
\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
\n" ); document.write( "
\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-12%29%5E2-4%2A4%2A9=0\".
\n" ); document.write( "
\n" ); document.write( " Discriminant d=0 is zero! That means that there is only one solution: \"x+=+%28-%28-12%29%29%2F2%5C4\".
\n" ); document.write( " Expression can be factored: \"4x%5E2%2B-12x%2B9+=+4%28x-1.5%29%2A%28x-1.5%29\"
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\n" ); document.write( " Again, the answer is: 1.5, 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+4%2Ax%5E2%2B-12%2Ax%2B9+%29\"

\n" ); document.write( "\n" ); document.write( ".
\n" ); document.write( "\"2x%5E2=128\"
\n" ); document.write( "\"x%5E2=64\"
\n" ); document.write( "\"x=8\" or \"x=-8\"
\n" ); document.write( ".
\n" ); document.write( "\"x%5E2%2B25=0\"
\n" ); document.write( "\"x%5E2=-25\"
\n" ); document.write( "\"x=5i\" or \"-5i\"
\n" ); document.write( ".
\n" ); document.write( "\"x%5E2=25%2F36\"
\n" ); document.write( "\"x=5%2F6\" or \"x=-5%2F6\"
\n" ); document.write( ".
\n" ); document.write( "\"0=6x%5E2-24\"
\n" ); document.write( "\"-6x%5E2=-24%7D%7D%0D%0A%7B%7B%7Bx%5E2=4\"
\n" ); document.write( "\"x=2\" or \"x=-2\"
\n" ); document.write( ".
\n" ); document.write( "\"2%28x%2B3%29%5E2-4=68\"
\n" ); document.write( "\"2%28x%5E2%2B6x%2B9%29-4=68\"
\n" ); document.write( "\"2x%5E2%2B12x%2B18-4-68\"
\n" ); document.write( "\"2x%5E2%2B12x-54=0\"
\n" ); document.write( "\"x%5E2%2B6x-27=0\"
\n" ); document.write( "\"x%5E2%2B9x-3x-27=0\"
\n" ); document.write( "\"%28x%5E2%2B9x%29%2B%28-3x-27%29=0\"
\n" ); document.write( "\"x%28x%2B9%29-3%28x%2B9%29=0\"
\n" ); document.write( "\"%28x-3%29%28x%2B9%29=0\"
\n" ); document.write( "\"x=3\" or \"x=-9\"
\n" ); document.write( ".
\n" ); document.write( "\"x%5E2%2B5x-24=0\"
\n" ); document.write( "\"x%5E2%2B8x-3x-24=0\"
\n" ); document.write( "\"%28x%5E2%2B8x%29%2B%28-3x-24%29=0\"
\n" ); document.write( "\"x%28x%2B8%29-3%28x%2B8%29=0\"
\n" ); document.write( "\"%28x-3%29%28x%2B8%29=0\"
\n" ); document.write( "\"x=3\" or \"x=-8\"
\n" ); document.write( ".
\n" ); document.write( "\"x%5E2-3x-28=0\"
\n" ); document.write( "\"%28x%5E2-7x%29%2B%284x-28%29=0\"
\n" ); document.write( "\"x%28x-7%29%2B4%28x-7%29=0\"
\n" ); document.write( "\"%28x%2B4%29%28x-7%29=0\"
\n" ); document.write( "\"x=-4\" or \"x=7\"
\n" ); document.write( ".
\n" ); document.write( "\"x%5E2-49=0\"
\n" ); document.write( "\"x%5E2=49\"
\n" ); document.write( "\"x=-7\" or \"x=7\"
\n" ); document.write( ".
\n" ); document.write( "\"5x%5E2-2x-7=0\"
\n" ); document.write( "\"%285x%5E2-7x%29%2B%285x-7%29=0\"
\n" ); document.write( "\"x%285x-7%29%2B1%285x-7%29=0\"
\n" ); document.write( "\"%28x%2B1%29%285x-7%29=0\"
\n" ); document.write( "\"x=-1\" or \"x=7%2F5\"
\n" ); document.write( ".
\n" ); document.write( "I do not know why the next problems are all under the square root sign, but i bet you can do those. Remember, no value that is negative should be under a square root sign when you are not dealing with complex solutions.
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