Question

Complete the square for 3x2 - 12x = 9.

Answer 1

`3x^2-12x=9\\x^2-4x=3\\x^2-4x+4=7\\(x-2)^2=7\\x-2=\sqrt7 \vee x-2=-\sqrt7\\x=2+\sqrt7\vee x=2-\sqrt7`

Answer 2

`x=2 \pm √(7)`

Explanation:

Given this form ax^2+bx=k, here are my steps for completing the square while answer your question:

First step: Divide both sides by what is in front of x^2. You want the coefficient of x^2 to be 1. To do this for your question, divided both sides by 3.

This gives us x^2-4x = 3.

Second step: We are ready to begin the completing the square process at this step. We are going to add (b/2)^2 on both sides. For this question b=-4.

So we will be adding (-4/2)^2 on both sides.

This gives us x^2-4x+(-4/2)^2=3+(-4/2)^2.

Third step: I like to simplified the things inside the square and I do not actually apply the square at this step. It makes a later step easier in my opinion.

So this step gives us x^2-4x+(-2)^2=3+(-2)^2.

Fourth step: I'm actually going to write the left hand side as a square. Just drag the things that are inside the squares down into ( )^2.

This is what I mean x^2-4x+(-2)^2=(x-2)^2.

So at the end of this step we have (x-2)^2=3+(-2)^2.

Fifth step: I'm going to simplify the right hand side.

This step gives us (x-2)^2=7

Sixth step: We are ready to square root both sides.

This gives us
`x-2=\pm √(7)`

Seveth step: Get x by itself like you normally would with a linear equation. My step here is just to add 2 on both sides.

Final answer:
`x=2 \pm √(7)`