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

Step-by-step 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

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  

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)