Question 639486
 the possible choices: {{{20/9=2.22}}}, {{{7/9=0.77}}}, {{{-7/9=-0.77}, {{{-8/9=-0.88}}}, and {{{-20/9=-2.22}}} 

If {{{3x^2 - 2x + 7 = 0}}}, then {{{(x-1/3)^2}}} =?

{{{x = (-(-2) +- sqrt( (-2)^2-4*3*7 ))/(2*3) }}} 

{{{x = (2 +- sqrt( 4-84 ))/6 }}} 

{{{x = (2 +- sqrt( -80))/6 }}} 

{{{x = (2 +- 8.9i)/6 }}} 

solutions:

{{{x = (2 +8.9i)/6 }}} 

{{{x = 2/6 +8.9i/6 }}} 

{{{x = 0.3333 +1.4833i }}} 

or

{{{x = (2 -8.9i)/6 }}} 

{{{x = 2/6 -8.9i/6 }}} 

{{{x = 0.3333 -1.4833i }}} 

then {{{(x-1/3)^2}}} for {{{x = 0.3333 +1.4833i }}}  is

{{{(0.3333 +1.4833i-1/3)^2}}}

={{{(0.3333 +1.4833i-0.33)^2}}}

={{{(cross(0.3333) +1.4833i-cross(0.3333))^2}}}

={{{(1.4833i)^2}}}

={{{(1.4833)^2(i)^2}}}

={{{(2.2)(-1)}}}

={{{highlight(-2.2)}}}

and, another solution:

{{{(x-1/3)^2}}} for {{{x = 0.33 -1.48i }}}  is


{{{(0.3333 -1.4833i-1/3)^2}}}

={{{(0.3333 -1.4833i-0.3333)^2}}}

={{{(cross(0.3333) -1.4833i-cross(0.3333))^2}}}

={{{(-1.4833i)^2}}}

={{{(-1.4833)^2(i)^2}}}

={{{(-2.2)(-1)}}}

={{{highlight(2.2)}}}