solving a quadratic equation by completing the square

solving a quadratic equation by completing the square

 solve 2x² -4x -7 = 0 

 the equation can be written as 2x² -4x =7 

 dividing by 2 ( coefficient of x² )

 x² - 2 x = (7/2) 

note that coefficient of x is -2, take half of it that is -1,

 square that and add the square to both sides,

 use that to complete the square on the LHS x² - 2 x + 1² = (7/2) + 1²

 

 (x-1)² = (9/2) 

 

 take square root x -1 = ± ( 3 / √2 )

 

 x = 1 ± ( 3 / √2 ) 

 

 

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