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Completing the square is one of the three methods (quadratic factorisation and the quadratic formula being the other two) used to solve a quadratic equation, such as $ x^2 + 4x + 4 $.

The Aim: to write the equation in the form

$ (x+a)^2 = b $

ExampleEdit

$ x^2 + 10x = 52 $


First fill in with half of the 10 $ (x+5)^2 $


Expand the brackets

$ x^2 + 10x + 25 = 52 + 25 $i belive that at the bottom, it should be -3..77 .


$ (x+5)^2 = 77 $


$ x + 5 = \pm \sqrt{77} $


$ x = \pm \sqrt{77} - 5 $


$ x = 3.77 or -13.8 (3s.f.) $