Question

Use the quadratic formula to determine the exact solutions to the equation.

Answer 1

Answer:  " x = 1  + √5 " or " x = 1 − √5" .
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Given:
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   " x² − 2x − 4 = 0 " ;
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Solve for "x" by using the "quadratic formula" :

Note:  This equation is already written in "quadratic format" ; that is:

  " ax² + bx + c = 0 " ;  { "a $\neq$ 0" } ;

in which:   "a = 1" {the implied coefficient of "1" ;
                         since "1", multiplied by any value, equals that same value};

                 "b = -2 " ;

                 "c = -4 " ;
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The quadratic equation formula:

x = { - b ± √(b² − 4 ac) } / 2a ;   {"a$\neq$0"} ;
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Substitute our known values:
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   →  x = { - (-2) ± √[(-2)² − 4(1)(-4)] } / 2(1) ; 

       →  x  = { 2 ± √(4 − 4(-4) } / 2 ; 

       →  x  = { 2 ± √(4 − (-16) } / 2 ;

       →  x  = { 2 ± √(4 + 16) } / 2 ;

       →  x  = { 2 ± √(20) } / 2 ;

       →  x  = { 2 ± √4 √5} / 2 ;

       →  x  = { 2 ± 2√5} / 2 ;

       →  x = 1 ± √5 ; 

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→  "x = 1 + √5"  or  "x = 1 − √5" .
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