Solving Quadratic Equations Using The Method Of Completing The Square: Analysis And Applications

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1 Solving Quadratic Equations Using the Method of Completing the Square: Analysis and Applications Introduction The process of solving quadratic equation used in the following projects is the method of complete square. What we do is we form a complete square of a form (αx + β) 2 ,where x is the unknown and α & β being 2 suitable real numbers such that the left hand side of the equation contains only (αx + β ) 2 and the rest i.e. the right hand side of the equation contains only constant terms. Taking a general case for solving the equation, x 2 + ax + b = 0 x 2 + ax + b = Multiplying 4 both sides, 4x 2 + 4ax + 4b = 0 4x 2 + 4ax = - 4b In order to make the left hand side a square term, we add a 2 on both sides. 4x 2 + 4ax + a 2 = - 4b + a 2 (2x + a) 2 = - 4b + a 2 = c 2 (say) (2x + a) 2 = c 2 2x + a = ±c So, we get two linear equations for x, which we can solve to obtain the values of x. Here, α= 2, β = a are constants and the term on right hand side i.e. c 2 = a 2 – 4b is also constant.
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