##### 15.4 Solving quadratic equations by completing the square

### Solving quadratic equations by completing the square

When a quadratic equation cannot be factorized, we can use the method of completing the square to solve the equation.

#### Lessons

###### Notes:

###### 4-step approach:

1. isolate X’s on one side of the equation

2. factor out the __leading coefficient__ of $X^2$

3. “completing the square”

• X-side: inside the bracket, add (half of the coefficient of $X)^2$

• Y-side: add [ __leading coefficient__ $\cdot$ (half of the coefficient of $X)^2$ ]

4. clean up

• X-side: convert to perfect-square form

• Y-side: clean up the algebra

__leading coefficient__

__leading coefficient__