no idea

how do i write x squared - 6x+3 in the form (x+a) sqaured +b

 

x^2 -6x + 3 =

-(-x+sqrt(6)+3) (x+sqrt(6)-3)

To write     x² - 6x + 3     into the form     (x + a)² + b:

 

Complete the square of the part  x² - 6x  by adding 9     --->     x² - 6x + 9  =  (x - 3)²

 

However, you cannot change the value of the expression, so if you add 9, you must also subtract 9

--->      (x² - 6x) + 3     --->      (x² - 6x + 9) - 9 + 3      --->     (x² - 6x + 9) - 6     --->     (x - 3)² - 6

 

So:   x² - 6x + 3   becomes   (x - 3)² - 6

This means that in   (x + a)² + b   the 'a' has value -3   and  the 'b' has value -6.

 

Note:  to complete the square of  x² - 6x  divide the coefficient of the 'x' term by 2 and square that value.

-6 / 2  =  -3   and  (-3)²  =  9