Question

Solve each equation below by completing the square:

1) x^2 + 6x = 16
My steps:
x^2 + 6x - 16 = 0
(x - 2 )(x + 8)
x = 2, -8

I set it to zero and factored it out. But my teacher said not do it that way and do it by dividing by 2 but I don't understand how that works. I got the right answer but not the right way to solve it? If someone could explain how to do it by dividing it by 2, that would be awesome. Thank you!

Answer 1

you were supposed to complete the square.

x^2 + 6x = 16
x^2 + 6x + 9 = 16+9
(x+3)^2 = 25
x+3 = ±5
x = -3±5

and you get your solution.

To complete the square, you divide the coefficient of x by 2, since (x+a)^2 = a^2+2ax+a^2.

Answer 2

(x+a)^2 = x^2+2ax+a^2

Answer 3

I know I got the x = 2 -8 correct so I don't understand how you got x = -3±5 or where the 9 came from.

Answer 4

Look. You had

x^2+6x

If you consider that as x^2+2ax, a=3.

to complete the square, you have to add a^2, which is 9.

Just follow the steps I took in my solution. I assume you can take the square root of 25 when you get that far...