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complete the square;x^2-2x

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2 Answers

 It is required to complete the square root

x-2x

= (x2 -2x+1)-1        (adding and subracting 1)

= (x-1)2 - 1         because  ( x-y)2 = x2 +y2 -2xy

and here we get the result

I hope it helps !!

Hello Shelby,

Recall your algebraic identities

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

                      (x - y)2 = x2 - 2xy + y2

We will use these identities to do Completing the square. We have x2 - 2x

To make it a perfect square we will do 2y = -2, so we get y = -1, add square of y to make it a perfect square. y2 = 1. So, we have x2 - 2x + 1 = (x - 1)2 (answer)

To generalize this to any quadratic function of the form x2 + bx. In this, we have 2y = b which gives

y = b/2. Therefore,

x2 + bx + (b/2)2 = (x + (b/2))2

Quadratic function of the form x2 - bx. In this, we have 2y = -b which gives y = -b/2. Therefore,

x2 - bx + (-b/2)2 = (x - (-b/2))2

I hope this helps.

 

Woodbridge complete the square tutors