Question 200569
One  way  to  solve  eqn  without  formal  techniques  is  a  modified  graphing  technigue
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-x^2 +4x +5 =0
mult  thru  by  -1
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x^2 -4x -5 =0,,,,(could  have left  it  alone  but  personal  preference  is  to  have x^2  a  positive )
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We  are  looking  for  which  x"s  make  this  expression  = 0
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Let  D = x^2 -4x -5,,,make  a  T BOx
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X,,,,,,,,,,,,,,D
0.............-5
1,,,,,,,,,,,,,-8
2,,,,,,,,,,,,,-5
3,,,,,,,,,,,,,-8
4,,,,,,,,,,,,,-4
5,,,,,,,,,,,,,0,,,,,,,,,one  answer
6,,,,,,,,,,,,,,7
-1,,,,,,,,,,,,,0,,,,,,,,another  answer
-2,,,,,,,,,,,,7
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If  a  rough  plot  is  made,  we  see  a  y  parabola ,  pointed  up, with  vertex  at  (2,-9)
x  intercepts  at  x=-1,  x=+5
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Have  a  nice  day