document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=214941>Question 214941</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of each side of a square is increased by 4 in. The sum of the areas of the original square and the larger square is 106 in^2. What is the length of a side of the original square? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #162402 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=162402\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The length of each side of a square is increased by 4 in. The sum of the areas of the original square and the larger square is 106 in^2. What is the length of a side of the original square?\r<BR>\n" );
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document.write( "Step 1.  Let s be the length of the side of the original square then Area A of a square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=s%5E2 ALIGN=MIDDLE  ALT=\"A=s%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Step 2.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28s%2B4%29%5E2 ALIGN=MIDDLE  ALT=\"%28s%2B4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Area of square with side increased by 4.\r<BR>\n" );
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document.write( "Step 3.  Then using the problem statement where the sum of the areas of the two squares is 106 square inches, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2%2B%28s%2B4%29%5E2=106 ALIGN=MIDDLE  ALT=\"s%5E2%2B%28s%2B4%29%5E2=106\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "{{2{s^2+8s+16=106}}}\r<BR>\n" );
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document.write( "Step 4.  Subtract 106 from both sides 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=2s%5E2%2B8s%2B16-106=106-106 ALIGN=MIDDLE  ALT=\"2s%5E2%2B8s%2B16-106=106-106\"   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=2s%5E2%2B8s-90=0 ALIGN=MIDDLE  ALT=\"2s%5E2%2B8s-90=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 5.  We can now use the quadratic formula to solve this 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=2, b=8 and c=-90\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=as%5E2%2Bbs%2Bc=0 ALIGN=MIDDLE  ALT=\"as%5E2%2Bbs%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2s%5E2%2B8s%2B-90+=+0 ALIGN=MIDDLE  ALT=\"2s%5E2%2B8s%2B-90+=+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=s%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"s%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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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" );
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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=%288%29%5E2-4%2A2%2A-90=784 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%288%29%5E2-4%2A2%2A-90=784\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  Discriminant d=784 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+=+%28-8%2B-sqrt%28+784+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-8%2B-sqrt%28+784+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5B1%5D+=+%28-%288%29%2Bsqrt%28+784+%29%29%2F2%5C2+=+5 ALIGN=MIDDLE  ALT=\"s%5B1%5D+=+%28-%288%29%2Bsqrt%28+784+%29%29%2F2%5C2+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5B2%5D+=+%28-%288%29-sqrt%28+784+%29%29%2F2%5C2+=+-9 ALIGN=MIDDLE  ALT=\"s%5B2%5D+=+%28-%288%29-sqrt%28+784+%29%29%2F2%5C2+=+-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2s%5E2%2B8s%2B-90 ALIGN=MIDDLE  ALT=\"2s%5E2%2B8s%2B-90\"   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=2s%5E2%2B8s%2B-90+=+2%28s-5%29%2A%28s--9%29 ALIGN=MIDDLE  ALT=\"2s%5E2%2B8s%2B-90+=+2%28s-5%29%2A%28s--9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 5, -9.\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+2%2Ax%5E2%2B8%2Ax%2B-90+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B8%2Ax%2B-90+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Select the positive solution of s=5.  \r<BR>\n" );
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document.write( "As a check, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2%2B%28s%2B4%29%5E2=+25%2B81=106 ALIGN=MIDDLE  ALT=\"s%5E2%2B%28s%2B4%29%5E2=+25%2B81=106\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So it works!\r<BR>\n" );
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document.write( "Step 6.  The length of the original square is 5 inches.\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 http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit 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\r<BR>\n" );
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document.write( " </SPAN>\n" );
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