Question 700974
{{{ -x^2 + 7x = 8 }}}
{{{ -x^2 + 7x - 8 = 0 }}}
The quadratic formula finds 2 values for {{{ x }}} 
called the roots that satisfy this equation.
The equation has to be in the general form
{{{ ax^2 + b*x + c = 0 }}}
For your equation:
{{{ a = -1 }}}
{{{ b = 7 }}}
{{{ c = -8 }}}
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{{{ x = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}} 
{{{ x = ( -7 +- sqrt( 7^2 - 4*(-1)*(-8) )) / (2*(-1)) }}} 
{{{ x = ( -7 +- sqrt( 49 - 32)) / (-2) }}} 
{{{ x = ( -7 +- sqrt( 17)) / (-2) }}} 
{{{ x = ( -7 + 4.1231 ) / (-2) }}} 
{{{ x = -2.8769 / (-2) }}}
{{{ x = 1.4384 }}}
and 
{{{ x = ( -7 - 4.1231)/ (-2) }}} 
{{{ x = -11.1231 / (-2) }}}
{{{ x = 5.5616 }}}
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Check the solutions
{{{ -x^2 + 7x = 8 }}}
{{{ -(1.4384)^2 + 7*(1.4384) = 8 }}}
{{{ -2.069 + 10.0688 = 8 }}}
{{{ 7.9998 = 8 }}}
close enough
{{{ -(5.5616)^2 + 7*5.5616 = 8 }}}
{{{ -30.9314 + 38.9312 = 8 }}}
{{{ 7.9998 = 8 }}}
OK
Here's the plot of the equation:
{{{ graph( 400, 400, -5, 10, -10, 5, -x^2 + 7x - 8 ) }}}