Completing Square

Formula:

(x+y)2=x2+2.x.y+y2

(xy)2=x22.x.y+y2

Example 01

Convert x2+6x+7 to the form of (x+p)2+q

x2+6x+7x2+2.3.x+3232+7Form x2+2.3.x+32=(x+3)2(x+3)232+7(x+3)29+7(x+3)22


Example 02

Convert x28x+20 to the form of (x+p)2+q

x28x+20x22.4.x+4242+20Form x22.4.x+42=(x4)2(x4)242+20(x4)216+20(x4)2+4

Exercise

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