Question 338445
{{{m^2+2m=6}}} Start with the given equation.



{{{m^2+2m-6=0}}} Subtract 6 from both sides.



Notice that the quadratic {{{m^2+2m-6}}} is in the form of {{{Am^2+Bm+C}}} where {{{A=1}}}, {{{B=2}}}, and {{{C=-6}}}



Let's use the quadratic formula to solve for "m":



{{{m = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{m = (-(2) +- sqrt( (2)^2-4(1)(-6) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=2}}}, and {{{C=-6}}}



{{{m = (-2 +- sqrt( 4-4(1)(-6) ))/(2(1))}}} Square {{{2}}} to get {{{4}}}. 



{{{m = (-2 +- sqrt( 4--24 ))/(2(1))}}} Multiply {{{4(1)(-6)}}} to get {{{-24}}}



{{{m = (-2 +- sqrt( 4+24 ))/(2(1))}}} Rewrite {{{sqrt(4--24)}}} as {{{sqrt(4+24)}}}



{{{m = (-2 +- sqrt( 28 ))/(2(1))}}} Add {{{4}}} to {{{24}}} to get {{{28}}}



{{{m = (-2 +- sqrt( 28 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{m = (-2 +- 2*sqrt(7))/(2)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{m = (-2)/(2) +- (2*sqrt(7))/(2)}}} Break up the fraction.  



{{{m = -1 +- sqrt(7)}}} Reduce.  



{{{m = -1+sqrt(7)}}} or {{{m = -1-sqrt(7)}}} Break up the expression.  



So the solutions are {{{m = -1+sqrt(7)}}} or {{{m = -1-sqrt(7)}}} 



If you need more help, email me at <a href="mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help">jim_thompson5910@hotmail.com</a>


Also, feel free to check out my tutoring <a href="http://www.freewebs.com/jimthompson5910/home.html">website</a>. 


Jim