Question 373991
Is the equation {{{6x^2+11x+60=0}}} ??? If so, then...






{{{6x^2+11x+60=0}}} Start with the given equation.



Notice that the quadratic {{{6x^2+11x+60}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=6}}}, {{{B=11}}}, and {{{C=60}}}



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



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



{{{x = (-(11) +- sqrt( (11)^2-4(6)(60) ))/(2(6))}}} Plug in  {{{A=6}}}, {{{B=11}}}, and {{{C=60}}}



{{{x = (-11 +- sqrt( 121-4(6)(60) ))/(2(6))}}} Square {{{11}}} to get {{{121}}}. 



{{{x = (-11 +- sqrt( 121-1440 ))/(2(6))}}} Multiply {{{4(6)(60)}}} to get {{{1440}}}



{{{x = (-11 +- sqrt( -1319 ))/(2(6))}}} Subtract {{{1440}}} from {{{121}}} to get {{{-1319}}}



{{{x = (-11 +- sqrt( -1319 ))/(12)}}} Multiply {{{2}}} and {{{6}}} to get {{{12}}}. 



{{{x = (-11 +- i*sqrt(1319))/(12)}}} 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>)  



{{{x = (-11+i*sqrt(1319))/(12)}}} or {{{x = (-11-i*sqrt(1319))/(12)}}} Break up the expression.  



So the solutions are {{{x = (-11+i*sqrt(1319))/(12)}}} or {{{x = (-11-i*sqrt(1319))/(12)}}}