document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115339>Question 115339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the directions on this work sheet is use the quadratic formula to solve each equation and the equation is m^2+5m-6=0 i dont understand how to figure it out so if you could give me directions so that i know how to get the answer i would be greatly appriciated! thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83918 by </B><A HREF=/tutors/aboutme.mpl?userid=aka042><B>aka042(26)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=aka042><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=83918\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is in response to a follow up from the student to clarify.  My original solution remains below:\r<BR>\n" );
document.write( "\n" );
document.write( "m actually equals two numbers, 1 and - 6.\r<BR>\n" );
document.write( "\n" );
document.write( "The quadratic equation deals with the coefficients of the equation you are trying to solve.  Your equation is some coefficient a * m^2 + some coefficient b * m - 6, which we will call c.  Remember that a coefficient is the number that falls before your x term.  We have two x terms, x^2 and x, so two coefficients, a and b.\r<BR>\n" );
document.write( "\n" );
document.write( "In general form, the quadratic equation states that m = ( b + or - the square root of (b^2 - 4ac)) all divided by 2*a.\r<BR>\n" );
document.write( "\n" );
document.write( "So the quadratic equation first tells you to first solve for b^2 - 4 * a * c.  For your specific equation: b, the number that appears before \"m\", is 5.  a, the number that appears before m^2, is 1.  And finally c, is -6.  Therefore b^2 = 5^2 = 25, and 4 * a * c = 4 * 1 * -6 = -24.  So b^2 - 4*a*c = 25 - (-24) = 25 + 24 = 49.\r<BR>\n" );
document.write( "\n" );
document.write( "Next, we need to take the square root of that.  The square root of 49 is 7.\r<BR>\n" );
document.write( "\n" );
document.write( "After this, we need to split into two different equations: -b + 7 and -b - 7.  Knowing that b is 5, -b must be -5, so we have -5 + 7 =2 and -5 - 7 = -12.\r<BR>\n" );
document.write( "\n" );
document.write( "Finally, we need to divide both equations by 2 * a, or 2*1 = 2.  2/2 = 1, so your first solution is 1.  -12/2 = -6, so your second solution is -6.  Your answer is m = 1 and m = -6.\r<BR>\n" );
document.write( "\n" );
document.write( "Let's plug in to make sure:  1(1)^2 + 5(1) - 6 = 1 + 5 - 6 = 6- 6 = 0.  This fits your original equation so 1 is definitely a solution.<BR>\n" );
document.write( "1(-6)^2 + 5(-6) - 6 = 36 - 30 - 6 = 6 - 6 = 0, so -6 is also definitely a solution.\r<BR>\n" );
document.write( "\n" );
document.write( "Therefore your answers are m = 1 and m = -6.\r<BR>\n" );
document.write( "\n" );
document.write( "It may be a little confusing that an equation yields two solutions.  However, what you are doing is solving for when the given parabola crosses the line x= 0.  Since a parabola is symmetrical, this happens two times, yielding two solutions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Quadratic equations are typically expressed in terms of x, however the variable you use does not matter (in this case m).\r<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=am%5E2%2Bbm%2Bc=0 ALIGN=MIDDLE  ALT=\"am%5E2%2Bbm%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1m%5E2%2B5m%2B-6+=+0 ALIGN=MIDDLE  ALT=\"1m%5E2%2B5m%2B-6+=+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=m%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"m%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=%285%29%5E2-4%2A1%2A-6=49 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%285%29%5E2-4%2A1%2A-6=49\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=49 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+=+%28-5%2B-sqrt%28+49+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-5%2B-sqrt%28+49+%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=m%5B1%5D+=+%28-%285%29%2Bsqrt%28+49+%29%29%2F2%5C1+=+1 ALIGN=MIDDLE  ALT=\"m%5B1%5D+=+%28-%285%29%2Bsqrt%28+49+%29%29%2F2%5C1+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D+=+%28-%285%29-sqrt%28+49+%29%29%2F2%5C1+=+-6 ALIGN=MIDDLE  ALT=\"m%5B2%5D+=+%28-%285%29-sqrt%28+49+%29%29%2F2%5C1+=+-6\"   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=1m%5E2%2B5m%2B-6 ALIGN=MIDDLE  ALT=\"1m%5E2%2B5m%2B-6\"   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=1m%5E2%2B5m%2B-6+=+1%28m-1%29%2A%28m--6%29 ALIGN=MIDDLE  ALT=\"1m%5E2%2B5m%2B-6+=+1%28m-1%29%2A%28m--6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1, -6.\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%2B5%2Ax%2B-6+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );