Question 472171


{{{-x^2+7x-4=0}}} Start with the given equation.



Notice that the quadratic {{{-x^2+7x-4}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=-1}}}, {{{B=7}}}, and {{{C=-4}}}



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



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



{{{x = (-(7) +- sqrt( (7)^2-4(-1)(-4) ))/(2(-1))}}} Plug in  {{{A=-1}}}, {{{B=7}}}, and {{{C=-4}}}



{{{x = (-7 +- sqrt( 49-4(-1)(-4) ))/(2(-1))}}} Square {{{7}}} to get {{{49}}}. 



{{{x = (-7 +- sqrt( 49-16 ))/(2(-1))}}} Multiply {{{4(-1)(-4)}}} to get {{{16}}}



{{{x = (-7 +- sqrt( 33 ))/(2(-1))}}} Subtract {{{16}}} from {{{49}}} to get {{{33}}}



{{{x = (-7 +- sqrt( 33 ))/(-2)}}} Multiply {{{2}}} and {{{-1}}} to get {{{-2}}}. 



{{{x = (-7+sqrt(33))/(-2)}}} or {{{x = (-7-sqrt(33))/(-2)}}} Break up the expression.  



So the solutions are {{{x = (-7+sqrt(33))/(-2)}}} or {{{x = (-7-sqrt(33))/(-2)}}} 



These solutions approximate to {{{x = 0.62771867673099}}} or {{{x = 6.37228132326901}}}