Question 499743


{{{9x^2+11x+18=-10x+8}}} Start with the given equation.



{{{9x^2+11x+18+10x-8=0}}} Get every term to the left side.



{{{9x^2+21x+10=0}}} Combine like terms.



Notice that the quadratic {{{9x^2+21x+10}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=9}}}, {{{B=21}}}, and {{{C=10}}}



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



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



{{{x = (-(21) +- sqrt( (21)^2-4(9)(10) ))/(2(9))}}} Plug in  {{{A=9}}}, {{{B=21}}}, and {{{C=10}}}



{{{x = (-21 +- sqrt( 441-4(9)(10) ))/(2(9))}}} Square {{{21}}} to get {{{441}}}. 



{{{x = (-21 +- sqrt( 441-360 ))/(2(9))}}} Multiply {{{4(9)(10)}}} to get {{{360}}}



{{{x = (-21 +- sqrt( 81 ))/(2(9))}}} Subtract {{{360}}} from {{{441}}} to get {{{81}}}



{{{x = (-21 +- sqrt( 81 ))/(18)}}} Multiply {{{2}}} and {{{9}}} to get {{{18}}}. 



{{{x = (-21 +- 9)/(18)}}} Take the square root of {{{81}}} to get {{{9}}}. 



{{{x = (-21 + 9)/(18)}}} or {{{x = (-21 - 9)/(18)}}} Break up the expression. 



{{{x = (-12)/(18)}}} or {{{x =  (-30)/(18)}}} Combine like terms. 



{{{x = -2/3}}} or {{{x = -5/3}}} Simplify. 



So the solutions are {{{x = -2/3}}} or {{{x = -5/3}}}