Question

Which equation is equivalent to the following?

4x^2 + 4y^2 +16x – 24y = 34
Please answer it:(

Answer 1

The correct answer is the third expression.

Explanation:

We have the following equation:

`4*x^2 + 4*y^2 + 16*x - 24*y = 34`

Let's organize it by variables, putting together the ones that have the same letter or no letter at all. We have:

`4*x^2 + 16*x + 4*y^2 - 24*y = 34`

We can extract the common factor on the left side by dividing them by 4, we have:

`4*(x^2 + 4*x) + 4*(y^2 - 6*y) = 34`

We need to complete the squares on the parenthesis without changing the value of the equation, to do that we will sum the proper values inside the parenthesis and those multiplied by four on the other side of the equation, we have:

`4*(x^2 + 4*x + 4) + 4*(y^2 - 6*y + 9) = 34 + 16 + 36\\4*(x + 2)^2 + 4*(y - 3)^2 = 86`

The correct answer is the third expression.