Question 227578

{{{9x^2=12x-2}}} Start with the given equation.



{{{9x^2-12x+2=0}}} Get every term to the left side.



Notice that the quadratic {{{9x^2-12x+2}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=9}}}, {{{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(9)(2) ))/(2(9))}}} Plug in  {{{A=9}}}, {{{B=-12}}}, and {{{C=2}}}



{{{x = (12 +- sqrt( (-12)^2-4(9)(2) ))/(2(9))}}} Negate {{{-12}}} to get {{{12}}}. 



{{{x = (12 +- sqrt( 144-4(9)(2) ))/(2(9))}}} Square {{{-12}}} to get {{{144}}}. 



{{{x = (12 +- sqrt( 144-72 ))/(2(9))}}} Multiply {{{4(9)(2)}}} to get {{{72}}}



{{{x = (12 +- sqrt( 72 ))/(2(9))}}} Subtract {{{72}}} from {{{144}}} to get {{{72}}}



{{{x = (12 +- sqrt( 72 ))/(18)}}} Multiply {{{2}}} and {{{9}}} to get {{{18}}}. 



{{{x = (12 +- 6*sqrt(2))/(18)}}} 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+6*sqrt(2))/(18)}}} or {{{x = (12-6*sqrt(2))/(18)}}} Break up the expression.  



{{{x = (2+sqrt(2))/(3)}}} or {{{x = (2-sqrt(2))/(3)}}} Reduce.  



So the solutions are {{{x = (2+sqrt(2))/(3)}}} or {{{x = (2-sqrt(2))/(3)}}}  



which approximate to {{{x=1.138}}} or {{{x=0.195}}}