Mathematics: 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

180Step-by-step explanation:...

Determine which equation has the same solutions

ashiteru123

15.03.2022

D. (x-3)^2=34

Step-by-step 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:

$x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2$ .

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

I'm going to add $(\frac{-6}{2})^2$ on both sides.

$x^2-6x+(\frac{-6}{2})^2-25=(\frac{-6}{2})^2$

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

$(x+\frac{-6}{2})^2-25=(-\frac{-6}{2})^2$

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

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