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 [tex] \neq [/tex] 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[tex] \neq [/tex]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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