document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172937>Question 172937</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321269470/algebrahomeworkh>Introductory Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation\r<BR>\n" );
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document.write( "sqrt (2x + 5) - sqrt (x - 2) = 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127829 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=127829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> although the answer is partially correct shown by monika  ..she is missing a solution and got fortunate(or unfortunate depending on how you see it) to find the solution of 2.  Why?? because when you do one thing to one side of the equation you have to do the same to the other....when you have one term to square on each side of the equals sign it is easy but when there are two terms which are added or subtracted......they must be taken as a whole and squared....you CANNOT square each term seperately unless the terms are multiplied together....with that in mind lets proceed to solve the problem. It is an easy mistake to make and is made quite often.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282x%2B5%29-sqrt%28x-2%29=3 ALIGN=MIDDLE  ALT=\"sqrt%282x%2B5%29-sqrt%28x-2%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >given<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282x%2B5%29-sqrt%28x-2%29%29%5E2=3%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%282x%2B5%29-sqrt%28x-2%29%29%5E2=3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >radicalize by squaring both sides <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B5-2%28sqrt%28%282x%2B5%29%28x-2%29%29%29%2Bx-2=9 ALIGN=MIDDLE  ALT=\"2x%2B5-2%28sqrt%28%282x%2B5%29%28x-2%29%29%29%2Bx-2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >multiplying out the squares<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B3-2%28sqrt%28%282x%2B5%29%28x-2%29%29%29=9 ALIGN=MIDDLE  ALT=\"3x%2B3-2%28sqrt%28%282x%2B5%29%28x-2%29%29%29=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > combining like terms on left side of eq<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%28sqrt%28%282x%2B5%29%28x-2%29%29%29=6-3x ALIGN=MIDDLE  ALT=\"-2%28sqrt%28%282x%2B5%29%28x-2%29%29%29=6-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" >combining like terms in the equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%28sqrt%28%282x%2B5%29%28x-2%29%29%29%29%5E2=%286-3x%29%5E2 ALIGN=MIDDLE  ALT=\"%28-2%28sqrt%28%282x%2B5%29%28x-2%29%29%29%29%5E2=%286-3x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >squaring both sides to radicalize again <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%282x%2B5%29%28x-2%29=36-36x%2B9x%5E2 ALIGN=MIDDLE  ALT=\"4%282x%2B5%29%28x-2%29=36-36x%2B9x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >squaring left removed radical...mult.right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%282x%5E2-4x%2B5x-10%29=36-36x%2B9x%5E2 ALIGN=MIDDLE  ALT=\"4%282x%5E2-4x%2B5x-10%29=36-36x%2B9x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >multiplied part of left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E2-16x%2B20x-40=36-36x%2B9x%5E2 ALIGN=MIDDLE  ALT=\"8x%5E2-16x%2B20x-40=36-36x%2B9x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >multiplied out rest of left side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-40x%2B76=0 ALIGN=MIDDLE  ALT=\"x%5E2-40x%2B76=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > combined like terms<BR>\n" );
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document.write( "answers<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=2%2Cx=38%29 ALIGN=MIDDLE  ALT=\"system%28x=2%2Cx=38%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=1x%5E2%2B-40x%2B76+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-40x%2B76+=+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" );
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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" );
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=%28-40%29%5E2-4%2A1%2A76=1296 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-40%29%5E2-4%2A1%2A76=1296\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1296 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--40%2B-sqrt%28+1296+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--40%2B-sqrt%28+1296+%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-%28-40%29%2Bsqrt%28+1296+%29%29%2F2%5C1+=+38 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-40%29%2Bsqrt%28+1296+%29%29%2F2%5C1+=+38\"   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-%28-40%29-sqrt%28+1296+%29%29%2F2%5C1+=+2 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-40%29-sqrt%28+1296+%29%29%2F2%5C1+=+2\"   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=1x%5E2%2B-40x%2B76 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-40x%2B76\"   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=1x%5E2%2B-40x%2B76+=+%28x-38%29%2A%28x-2%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-40x%2B76+=+%28x-38%29%2A%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 38, 2.\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+1%2Ax%5E2%2B-40%2Ax%2B76+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-40%2Ax%2B76+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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