Question 216865


{{{33x^2+10x-2=0}}} Start with the given equation.



Notice that the quadratic {{{33x^2+10x-2}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=33}}}, {{{B=10}}}, 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 = (-(10) +- sqrt( (10)^2-4(33)(-2) ))/(2(33))}}} Plug in  {{{A=33}}}, {{{B=10}}}, and {{{C=-2}}}



{{{x = (-10 +- sqrt( 100-4(33)(-2) ))/(2(33))}}} Square {{{10}}} to get {{{100}}}. 



{{{x = (-10 +- sqrt( 100--264 ))/(2(33))}}} Multiply {{{4(33)(-2)}}} to get {{{-264}}}



{{{x = (-10 +- sqrt( 100+264 ))/(2(33))}}} Rewrite {{{sqrt(100--264)}}} as {{{sqrt(100+264)}}}



{{{x = (-10 +- sqrt( 364 ))/(2(33))}}} Add {{{100}}} to {{{264}}} to get {{{364}}}



{{{x = (-10 +- sqrt( 364 ))/(66)}}} Multiply {{{2}}} and {{{33}}} to get {{{66}}}. 



{{{x = (-10 +- 2*sqrt(91))/(66)}}} 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 = (-10+2*sqrt(91))/(66)}}} or {{{x = (-10-2*sqrt(91))/(66)}}} Break up the expression.  



{{{x = (-5+sqrt(91))/(33)}}} or {{{x = (-5-sqrt(91))/(33)}}} Reduce



So the solutions are {{{x = (-5+sqrt(91))/(33)}}} or {{{x = (-5-sqrt(91))/(33)}}}



which approximate to {{{x=0.138}}} or {{{x=-0.441}}}