Question

Sienna is solving the quadratic equation by completing the square.

3x2 9x – 4 = 0

3x2 9x = 4

a(x2 3x) = 4

what is the value of a?

–4
–3
3
4

Answer 1

Answer: The correct option is (C) 3.

Step-by-step explanation: Given that Sienna is solving the quadratic equation by completing the square as follows:

`3x2+9x-4=0\\\\\Rightarrow 3x^2+9x=4\\\\\Rightarrow a(x^2+3x)=4.`

We are given to find the find the value of a.

We can see that in the second step of Sienna's solution, 3 is common in both the terms,
`3x2` and
`9x.`

So, she took 3 out and then in the third step, the expression within the bracket remais
`x^2+3x.`

Therefore, the complete steps are as follows:

`3x2+9x-4=0\\\\\Rightarrow 3x^2+9x=4\\\\\Rightarrow 3(x^2+3x)=4.`

Hence, the value of a is 3.

Thus, (C) is the correct option.

Answer 2

3x^2 + 9x - 4
3x^2 + 9x = 4
3(x^2 + 3x) = 4

Therefore, a = 3