complete the square;x^2-2x

Question

complete the square

 

Answer 1

 It is required to complete the square root

x²  -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 !!

Answer 2

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.