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

Get step-by-step Homework Answers on solving quadratic equations with completing the square.

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1Solving Quadratic Equations Using the Method of Completing the Square: Analysis andApplicationsIntroductionThe process of solving quadratic equation used in the following projects is the method of complete square.What we do is we form acomplete square of a form (αx + β)2,where x is the unknown and α & β being 2suitable real numbers such that the left hand side of the equation contains only (αx +β)2and the rest i.e.the right hand side of the equation contains only constant terms.Taking a general case for solving the equation, x2+ ax + b = 0x2+ ax + b =Multiplying 4 both sides,4x2+ 4ax + 4b = 04x2+ 4ax =-4bIn order to make the left hand side a square term,we add a2on both sides.4x2+ 4ax + a2=-4b + a2(2x + a)2=-4b + a2= c2(say)(2x + a)2= c22x + a = ±cSo, 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. c2= a2–4b is also constant.

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