Question 549064
{{{x^2+11=6x}}} Start with the given equation.



{{{x^2+11-6x=0}}} Get every term to the left side.



{{{x^2-6x+11=0}}} Rearrange the terms.



Notice that the quadratic {{{x^2-6x+11}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=-6}}}, and {{{C=11}}}



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



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



{{{x = (-(-6) +- sqrt( (-6)^2-4(1)(11) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-6}}}, and {{{C=11}}}



{{{x = (6 +- sqrt( (-6)^2-4(1)(11) ))/(2(1))}}} Negate {{{-6}}} to get {{{6}}}. 



{{{x = (6 +- sqrt( 36-4(1)(11) ))/(2(1))}}} Square {{{-6}}} to get {{{36}}}. 



{{{x = (6 +- sqrt( 36-44 ))/(2(1))}}} Multiply {{{4(1)(11)}}} to get {{{44}}}



{{{x = (6 +- sqrt( -8 ))/(2(1))}}} Subtract {{{44}}} from {{{36}}} to get {{{-8}}}



{{{x = (6 +- sqrt( -8 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (6 +- 2i*sqrt(2))/(2)}}} 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 = (6)/(2) +- (2i*sqrt(2))/(2)}}} Break up the fraction.  



{{{x = 3 +- i*sqrt(2)}}} Reduce.  



{{{x = 3+i*sqrt(2)}}} or {{{x = 3-i*sqrt(2)}}}  Break up the expression.  



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



If you need more help, email me at <a href="mailto:jim_thompson5910@hotmail.com">jim_thompson5910@hotmail.com</a>


Also, please consider visiting my website: <a href="http://www.freewebs.com/jimthompson5910/home.html">http://www.freewebs.com/jimthompson5910/home.html</a> and making a donation. Thank you


Jim