Question 1010344
{{{ 0 = -x^2 + b*x - 8 }}}
One solution means this parabola touches the 
x-axis at one point
The quadratic formula is:
 {{{ x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
Just get rid of the part that gives 2 solutions,
the +- part.
{{{ x = (-b )/(2*a) }}} 
{{{ x = (-b)/(-2) }}}
{{{ x = b/2 }}}
--------------
{{{ 0 = -(b/2)^2 + b*(b/2) - 8 }}}
{{{ 0 = -b^2/4 + b^2/2 - 8 }}}
{{{ 0 = b^2/4 - 8 }}}
{{{ b^2/4 = 8 }}}
{{{ b^2 = 32 }}}
{{{ b = 4*sqrt(2) }}}
{{{ b = -4*sqrt(2) }}}
-----------------
check the answers:
{{{ sqrt( b^2-4*a*c ) }}} must equal zero, so
{{{ b^2 = 4a*c }}}
{{{ ( 4*sqrt(2) )^2 = 4*( -1 )*(-8) }}}
{{{ 16*2 = 32 }}}
{{{ 32 = 32 }}}
and
{{{ b^2 = 4a*c }}}
{{{ ( -4*sqrt(2) )^2 = 4*( -1 )*(-8) }}}
{{{ 16*2 = 32 }}}
{{{ 32 = 32 }}}
OK
Here is the plot:
{{{ graph( 400, 400, -2, 10, -10, 2, -x^2 + 4*sqrt(2)*x - 8 ) }}}