Question 151911


{{{3x^2+9x=-4}}} Start with the given equation.



{{{3x^2+9x+4=0}}} Add 4 to both sides.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=3}}}, {{{b=9}}}, and {{{c=4}}}



Let's use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(9) +- sqrt( (9)^2-4(3)(4) ))/(2(3))}}} Plug in  {{{a=3}}}, {{{b=9}}}, and {{{c=4}}}



{{{x = (-9 +- sqrt( 81-4(3)(4) ))/(2(3))}}} Square {{{9}}} to get {{{81}}}. 



{{{x = (-9 +- sqrt( 81-48 ))/(2(3))}}} Multiply {{{4(3)(4)}}} to get {{{48}}}



{{{x = (-9 +- sqrt( 33 ))/(2(3))}}} Subtract {{{48}}} from {{{81}}} to get {{{33}}}



{{{x = (-9 +- sqrt( 33 ))/(6)}}} Multiply {{{2}}} and {{{3}}} to get {{{6}}}. 



{{{x = (-9+sqrt(33))/(6)}}} or {{{x = (-9-sqrt(33))/(6)}}} Break up the expression.  



So our answers are {{{x = (-9+sqrt(33))/(6)}}} or {{{x = (-9-sqrt(33))/(6)}}} 



which approximate to {{{x=-0.543}}} or {{{x=-2.457}}}