Question 589117
I'll pick a random quadratic:
{{{ 2x^2 - 9x + 24 }}}
Set equal to zero to find roots
{{{ 2x^2 - 9x + 24 = 0 }}}
Get the constant term on the right side
by subtracting {{{ 24 }}} from both sides
{{{ 2x^2 - 9x = -24 }}}
Divide both sides by {{{ 2 }}}
{{{ x^2 - (9/2)*x = -12 }}}
Now take 1/2 of the coefficient of {{{x}}},
divide it by {{{2}}}, square it, and add it
to both sides
{{{ x^2 - (9/2)*x + (9/4)^2 = -12 + (9/4)^2 }}}
The left side will automatically become a perfect square
{{{ ( x - 9/4 )^2 = -(192/16) + 81/16 }}}
{{{ ( x - 9/4 )^2 = -( 111/16 ) }}}
Now take the square root of both sides
{{{ x - 9/4 = sqrt( 1/16 )*sqrt( -111) }}}
{{{ x- 9/4 = (1/4)*10.536i }}}
{{{ x = (1/4)*( 9 + 10.536i ) }}}
and also, using the (-) square root,
{{{ x = (1/4)*( 9 - 10.536i ) }}}