Question

Which method would you choose to solve this equation? Justify your reasoning. x^2+6X-2=0
I know that I want to graph this but I am not sure how to justify my reasoning.

Answer 1

Complete the square?

Answer 2

i would complete the square as well because the "middle term" 6x has an even coefficient

Answer 3

then you do not get an annoying denominator forced on you by the quadratic formula

Answer 4

Thank you so much!

Answer 5

\[(x^2+6x=2\]
\[(x+3)^3=2+9=11\] etc

Answer 6

That should be (x+3)^2 though.

Answer 7

yeah right! don't know where the cube came from...

Answer 8

Is "completing the square" this method :
x^2+6X-2=0
x² + 2 *3 x -2 =0
x² + 2 *3 x + 3² - 3² -2 =0
(x+3)² -11 = 0
(x+3)² - Sqrt(11)² = 0
(x+2 - Sqrt(11)) * (x+2+Sqrt(11)) = 0
x = -2 + Sqrt(11), x = -2 - Sqrt(11)

Answer 9

Something like that, except I think you've overcomplicated it. From the fourth line you have:\[(x+3)^2=11\implies x+3=\pm\sqrt{11}\implies x=-3\pm\sqrt{11}\]

Answer 10

Thanks .