Question 762460
{{{ x^2 - 4x + 45 = 0 }}}
Subtract {{{ 45 }}} from both sides
{{{ x^2 - 4x = -45 }}}
Take 1/2 of the coefficient of the {{{x}}}
term, square it, and add it to both sides
{{{ x^2 - 4x + ( -4/2 )^2 = -45 + ( -4/2 )^2 }}}
Note that when minus is squared, it becomes positive
{{{ x^2 - 4x + ( -4/2 )^2 = -45 + ( -4/2 )^2 }}}
{{{ x^2  - 4x + 4 = -45 + 4 }}}
{{{ x^2 - 4x + 4 = -41 }}}
{{{ ( x - 2 )^2 = -41 }}}
Take the square root of both sides
{{{ x - 2 = sqrt( 41 )*i  }}}
{{{ x = 2 + sqrt( 41 )*i }}}
and, also
{{{ x - 2 = -sqrt( 41 )*i  }}}
{{{ x = 2 - sqrt( 41 )*i }}}
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This would have been much easier if the equation was
{{{ x^2 - 4x - 45 }}} -are you sure of the {{{ +45 }}}?