Question

Complete the square for 3x^2-12x=9

Answer 1

The solutions are -0.65 and 4.65.

Explanation:

3x^2 - 12x = 9

Divide both sides by 3

x^2 - 4x = 3

To make a square with "x^2 - 4x", you need to have a "+ 4" after it so it can be simplified as (x-2)^2. So add 4 to both sides.

x^2 - 4x + 4 = 7

(x-2)^2 = 7

x - 2 = (square root) of 7

x = 2 (+/-) (square root) of 7.

x = {-0.65, 4.65}

The solutions are -0.65 and 4.65.

hope this helps:)sorry if it doesnt

Answer 2

`(x-2)^2=7`

Explanation:

We have been given an equation
`3x^2-12x=9`. We are asked to complete the square for the given equation.

We know that when an equation is in form
`x^2+bx=c`, then we will add
`((b)/(2))^2` to both sides of equation to make a perfect square.

Dividing both sides by 3, we will get:

`x^2-4x=3`

Add
`((b)/(2))^2` on both sides of equation:

`((b)/(2))^2=((4)/(2))^2=2^2=4`

`x^2-4x+4=3+4`

`x^2-4x+4=7`

Now, apply perfect square formula
`a^2-2ab+b^2=(a-b)^2`:

`(x-2)^2=7`

Therefore, our required equation would be
`(x-2)^2=7`.