Q:

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

Accepted Solution

A:
Answer: [tex] x=2 \pm \sqrt{7} [/tex] 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=7Sixth step:  We are ready to square root both sides.  This gives us [tex] x-2=\pm \sqrt{7} [/tex]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:  [tex] x=2 \pm \sqrt{7} [/tex]