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


x^2 + 10x = 52

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

Expand the brackets

x^2 + 10x + 25 = 52 + 25i 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.)

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