X^2+6x-6=0 rewritten by completing the square

Hello from MrBillDoesMath!

(x+3)^2 -15 = 0

Discussion:

To complete the square add (and then subtract) the square of one-half the coefficient of x:

x^2 + 6x -6 = 0 =>

                 -- complete the square part --

x^2 + 6x +   (6/2)^2 - (6/2)^2                    - 6 = 0 =>

x^2 + 6x + 9 - 9 - 6 = 0 =>                                               as 6/2 = 3

(x + 3)^ 2      - 9  - 6 = 0 =>                                    

(x+3)^2 -15 = 0

We can solve this as follows:

(x+3)^2 = 15                                               take square root of both sides

(x+3) = +\- sqrt(15)

x = -3 +\- sqrt(15)

Thank you,

MrB

positive

step-by-step explanation:

the quadrant is facing upwards