Question

Determine which equation has the same solutions as the given equation

2x^2 - 12x - 50 = 0
A. (x-3)^2 = 16
B. (x - 6)^2 = 19
C. (x - 6)^2 = 31
D. (x - 3)^2 = 34

Answer 1

D.
`(x-3)^2=34`

Explanation:

Its looks like they have complete the square for the given equation.

So let's do that.

`2x^2-12x-50=0`

I see all of my terms are even so I can easily divide each of them by 2.

I'm going to divide both sides by 2:

`x^2-6x-25=0`

The first step in completing the square is to make sure the coefficient of
`x^2` is 1 so we can use this easy formula:

`x^2+kx+((k)/(2))^2=(x+(k)/(2))^2`.

So I see in place of k I have -6.

I'm going to add
`((-6)/(2))^2` on both sides.

`x^2-6x+((-6)/(2))^2-25=((-6)/(2))^2`

See these first three terms here can be written using the mentioned formula:

`(x+(-6)/(2))^2-25=(-(-6)/(2))^2`

Let's simplify a bit:

`(x+(-3))^2-25=(-3)^2`

`(x-3)^2-25=9`

Add 25 on both sides:

`(x-3)^2=9+25`

`(x-3)^2=34`

Answer 2

Explanation:

here is the answer ....feel free to ask if u don't get it