Question 188334
I'm assuming that the equation should be {{{600 = 0.9x^2 - 26.5x + 290}}}




{{{600 = 0.9x^2 - 26.5x + 290}}} Start with the given equation.



{{{6000 = 9x^2 - 265x + 2900}}} Multiply EVERY term by 10 to make every number a whole number



{{{0 = 9x^2 - 265x + 2900-6000}}} Subtract 6000 from both sides.



{{{0 = 9x^2 - 265x -3100}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=9}}}, {{{b=-265}}}, and {{{c=-3100}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(-265) +- sqrt( (-265)^2-4(9)(-3100) ))/(2(9))}}} Plug in  {{{a=9}}}, {{{b=-265}}}, and {{{c=-3100}}}



{{{x = (265 +- sqrt( (-265)^2-4(9)(-3100) ))/(2(9))}}} Negate {{{-265}}} to get {{{265}}}. 



{{{x = (265 +- sqrt( 70225-4(9)(-3100) ))/(2(9))}}} Square {{{-265}}} to get {{{70225}}}. 



{{{x = (265 +- sqrt( 70225--111600 ))/(2(9))}}} Multiply {{{4(9)(-3100)}}} to get {{{-111600}}}



{{{x = (265 +- sqrt( 70225+111600 ))/(2(9))}}} Rewrite {{{sqrt(70225--111600)}}} as {{{sqrt(70225+111600)}}}



{{{x = (265 +- sqrt( 181825 ))/(2(9))}}} Add {{{70225}}} to {{{111600}}} to get {{{181825}}}



{{{x = (265 +- sqrt( 181825 ))/(18)}}} Multiply {{{2}}} and {{{9}}} to get {{{18}}}. 



{{{x = (265 +- 5*sqrt(7273))/(18)}}} Simplify the square root 



{{{x = (265+5*sqrt(7273))/(18)}}} or {{{x = (265-5*sqrt(7273))/(18)}}} Break up the expression.  



So the answers are {{{x = (265+5*sqrt(7273))/(18)}}} or {{{x = (265-5*sqrt(7273))/(18)}}} 



which approximate to {{{x=38.412}}} or {{{x=-8.967}}}