document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=216488>Question 216488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the difference of two whole numbersis 2. if two times the squareof the smaller number added too three times the squareof the larger numbers equal 140, find the numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163506 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=163506\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The difference of two whole numbers is 2. if two times the square of the smaller number added too three times the square of the larger numbers equal 140, find the numbers.\r<BR>\n" );
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document.write( "Step 1.  Let x be one number and x+2 be the other number.\r<BR>\n" );
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document.write( "Step 2.  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+ ALIGN=MIDDLE  ALT=\"2x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > be two times the square of the smaller number.\r<BR>\n" );
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document.write( "Step 3.  Let 3*(x+2)^2 be three times the square of the larger number.\r<BR>\n" );
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document.write( "Step 4.  The, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B3%28x%2B2%29%5E2=140 ALIGN=MIDDLE  ALT=\"2x%5E2%2B3%28x%2B2%29%5E2=140\"   DISABLED_style= \"max-width:90%; height:auto;\" > since two times the square of the smaller number added too three times the square of the larger numbers equal 140.\r<BR>\n" );
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document.write( "Step 5.  Solving yields the following steps:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B3%28x%2B2%29%5E2=140 ALIGN=MIDDLE  ALT=\"2x%5E2%2B3%28x%2B2%29%5E2=140\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B3%28x%5E2%2B4x%2B4%29=140 ALIGN=MIDDLE  ALT=\"2x%5E2%2B3%28x%5E2%2B4x%2B4%29=140\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B3x%5E2%2B12x%2B12=140 ALIGN=MIDDLE  ALT=\"2x%5E2%2B3x%5E2%2B12x%2B12=140\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B12x%2B12=140 ALIGN=MIDDLE  ALT=\"5x%5E2%2B12x%2B12=140\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract 140 from both sides of the equation to get a quadratic equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B12x%2B12-140=140-140 ALIGN=MIDDLE  ALT=\"5x%5E2%2B12x%2B12-140=140-140\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B12x-128=0 ALIGN=MIDDLE  ALT=\"5x%5E2%2B12x-128=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 6. To solve, we can use the quadratic equation given as \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where a=5, b=12, and c=-128\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B12x%2B-128+=+0 ALIGN=MIDDLE  ALT=\"5x%5E2%2B12x%2B-128+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2812%29%5E2-4%2A5%2A-128=2704 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2812%29%5E2-4%2A5%2A-128=2704\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=2704 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-12%2B-sqrt%28+2704+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-12%2B-sqrt%28+2704+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+2704+%29%29%2F2%5C5+=+4 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+2704+%29%29%2F2%5C5+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%2812%29-sqrt%28+2704+%29%29%2F2%5C5+=+-6.4 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2812%29-sqrt%28+2704+%29%29%2F2%5C5+=+-6.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B12x%2B-128 ALIGN=MIDDLE  ALT=\"5x%5E2%2B12x%2B-128\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B12x%2B-128+=+5%28x-4%29%2A%28x--6.4%29 ALIGN=MIDDLE  ALT=\"5x%5E2%2B12x%2B-128+=+5%28x-4%29%2A%28x--6.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 4, -6.4.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B12%2Ax%2B-128+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B12%2Ax%2B-128+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Select the positive number since we want whole numbers gives x=4 and x+2=6\r<BR>\n" );
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document.write( "Check...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B3%28x%2B2%29%5E2=2%2A4%5E2%2B3%2A6%5E2=32%2B108=140 ALIGN=MIDDLE  ALT=\"2x%5E2%2B3%28x%2B2%29%5E2=2%2A4%5E2%2B3%2A6%5E2=32%2B108=140\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a true statement.\r<BR>\n" );
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document.write( "Step 7.  ANSWER: The numbers are 4 and 6.\r<BR>\n" );
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document.write( "I hope the above steps were helpful.\r<BR>\n" );
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document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit \r<BR>\n" );
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document.write( "http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit \r<BR>\n" );
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document.write( "http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "Good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J </SPAN>\n" );
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