This week, we learned how to solve quadratic equations by factoring, completing the square, and using the quadratic formula.

**Factoring**

Factoring and using the zero product property is one of the easiest ways to solve a quadratic formula, and it works with rational roots.

- A quadratic equation is any equation that can be written in the form a + bx + c= 0.
- Zero product property: if ab=0, then a=0 and b=0, or both a, b=0

*example*:

3 – 21x- 54= 0

- Factor, remembering CDPEU

3( – 7x- 18)= 0

- Use the zero product property

(x+2) (x-9)= 0

Either x+2= 0 or x-9= 0

x= -2, x= 9

**Completing the Square**

When the equation doesn’t factor, completing the square is a great way to solve the quadratic equation, and it works well with irrational roots.

- Rearrange the equation if the coefficient of is negative
- Make sure to get rid of the coefficient of by dividing each side by the coefficient (when the equation equals to 0)
- Move the constant term to the right of the equation
- complete the perfect square by dividing the 2nd term and multiplying and squaring it, and adding it to both sides of the equation
- factor the perfect square, and simplify the right side
- rake the square root of each side, and isolate the x

*example:*

12x= -2 + 54

2 + 12x= 54

+ 6x= 27

+ 6x + 9= 27+ 9

√ = √36

x-3= 6

x= 3 6

**Quadratic Formula**

The Quadratic formula is easy to use if it is arranged in the right form.

- Quadratic formula:
- Identify the values of a,b, and c( the coefficients) a + bx+ c= 0
- Plug a,b, and c in the formula and solve the equation

*example:*