Question 252256


{{{3x^2+12x=-2}}} Start with the given equation.



{{{3x^2+12x+2=0}}} Add 2 to both sides.



Notice that the quadratic {{{3x^2+12x+2}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=3}}}, {{{B=12}}}, and {{{C=2}}}



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



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



{{{x = (-(12) +- sqrt( (12)^2-4(3)(2) ))/(2(3))}}} Plug in  {{{A=3}}}, {{{B=12}}}, and {{{C=2}}}



{{{x = (-12 +- sqrt( 144-4(3)(2) ))/(2(3))}}} Square {{{12}}} to get {{{144}}}. 



{{{x = (-12 +- sqrt( 144-24 ))/(2(3))}}} Multiply {{{4(3)(2)}}} to get {{{24}}}



{{{x = (-12 +- sqrt( 120 ))/(2(3))}}} Subtract {{{24}}} from {{{144}}} to get {{{120}}}



{{{x = (-12 +- sqrt( 120 ))/(6)}}} Multiply {{{2}}} and {{{3}}} to get {{{6}}}. 



{{{x = (-12 +- 2*sqrt(30))/(6)}}} 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 = (-12+2*sqrt(30))/(6)}}} or {{{x = (-12-2*sqrt(30))/(6)}}} Break up the expression.  



{{{x = (-6+sqrt(30))/(3)}}} or {{{x = (-6-sqrt(30))/(3)}}} Reduce.



So the solutions are {{{x = (-6+sqrt(30))/(3)}}} or {{{x = (-6-sqrt(30))/(3)}}}



which approximate to {{{x=-0.174}}} or {{{x=-3.826}}}