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=7
Sixth 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]
