Question

2 Help

3x² +8x+ 5-14
Which constant would you add to the RIGHT side of the
quadratic equation in order to solve by completing the
square? Remember, this is a two-step process​

Answer 1

Answer: Option D.

Step-by-step explanation:

Given the quadratic equation
`3x^2+8x=-1`, you can observe that the leading coefficient is not 1, then you have to divide both sides of the equation by 3:

`(3x^2+8x)/(3)=(-1)/(3)\\\\x^2+(8)/(3)x=(-1)/(3)`

Now, you can observe that the coefficient of the x-term is
`(3)/(8)`, so you must divide it by 2 and square it. Then you get:

`(((8)/(3))/((2)/(1)))^2=(16)/(9)`

Therefore, you must add
`(16)/(9)` to both sides of the equation.

Answer 2

The correct answer is D

Step-by-step explanation

The given quadratic expression is

`3 {x}^(2) + 8x = - 1`

Divide through by 3

`{x}^(2) + (8)/(3) x = - (1)/(3)`

We now add the square of half the coefficient of x because the coefficient of the quadratic term is now unity.

The constant we would add is

`{( (4)/(3) )}^(2) = (16)/(9)`

The correct answer is D