Question 172426
{{{2(x-3)^2=-2x+9}}} Start with the given equation.



{{{2(x^2-6x+9)=-2x+9}}} FOIL



{{{2x^2-12x+18=-2x+9}}} Distribute



{{{2x^2-12x+18+2x-9=0}}} Get all terms to the left side.



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



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=2}}}, {{{b=-10}}}, and {{{c=9}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(-10) +- sqrt( (-10)^2-4(2)(9) ))/(2(2))}}} Plug in  {{{a=2}}}, {{{b=-10}}}, and {{{c=9}}}



{{{x = (10 +- sqrt( (-10)^2-4(2)(9) ))/(2(2))}}} Negate {{{-10}}} to get {{{10}}}. 



{{{x = (10 +- sqrt( 100-4(2)(9) ))/(2(2))}}} Square {{{-10}}} to get {{{100}}}. 



{{{x = (10 +- sqrt( 100-72 ))/(2(2))}}} Multiply {{{4(2)(9)}}} to get {{{72}}}



{{{x = (10 +- sqrt( 28 ))/(2(2))}}} Subtract {{{72}}} from {{{100}}} to get {{{28}}}



{{{x = (10 +- sqrt( 28 ))/(4)}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}. 



{{{x = (10 +- 2*sqrt(7))/(4)}}} 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 = (10+2*sqrt(7))/(4)}}} or {{{x = (10-2*sqrt(7))/(4)}}} Break up the expression.  



So the answers are {{{x = (10+2*sqrt(7))/(4)}}} or {{{x = (10-2*sqrt(7))/(4)}}} 



which approximate to {{{x=3.823}}} or {{{x=1.177}}}