Wednesday, December 21, 2011

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)1² = (9/2)

take square root

x -1 = ± ( 3 / √2 )

x = 1 ± ( 3 / √2 )


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