Nicoles be the professor

COMPLETING THE SQUARE:

 

This trick is used to factor quadratic expressions, especially when other methods (like the x-method) doesn’t work:

 

First you write your formula (ax² + bx + c) in the form ax² +bx= -c (move your c to the other side of the equation)

 

Divide b by 2, then square it (b/2)².

 

Add the (b/2)² to both sides of the equation: x² + bx + (b/2)² = -c + (b/2)².

 

Write the left side of the equation as a perfect square: [x + (b/2)]² = -c + (b/2)²

 

Let’s pretend that a=4, b=16, and c=-18

 

Move c to the right side of the equation to get 4x²+16x= 18

 

(-18 becomes positive when you move it to the right side)

 

Divide both sides of the equation by 4: x²+ 4x= 18/4.

 

Take ½ (4) which is the x term, and square it to get (4/2)²=4.

 

Add the 4 to both sides of the equation x²+ 4x +4= 18/4 + 4

 

Write the left side of the equation as (x+2)² which is a perfect square and you get that (x+2)²= 34/4

 

Then you’re done!!

 

Simple as that!

 

Well, not really, but if you do it a bunch, it eventually it will make sense. But only if you have a teacher who is patient and helpful like I do!!