1. Aim: How do we solve quadratic equations by completing square?
Do Now: 1. factor:
(x – 2)2 is called perfect square
2. Solve for x:
(x – 7)(x + 1) = 0, x = 7, –1
3. Solve for x:

2. Unlike # 2, Do Now #3, the trinomial is not factorable, therefore, we cannot solve it by factoring. A special method is needed to solve this type of equation.
The method we use is called completing square.
Move the constant to the right
Find the square of half the middle term
Both sides of the equation add the square of half middle term
(x – 3)2 = 2
Factor to complete the square for the left side
Take square root on both sides

3. Example : x2 + 6x + 2 = 0 x2 + 6x + ___= -2+___ x2 + 6x + 9 = -2 + 9
Move the constant.
x2 + 6x + ___= -2+___
Form a “perfect square”.
x2 + 6x + 9 =
Factor & Simplify.
(x + 3)2 = 7
(x + 3)2 = 7
Square root.
x + 3 = ± 7
x = -3 ± 7
Solve what is left.

4. x2 + 4x - = 0 + + 3 2 3 2 Solve for x: 2x2 +8x - 3 = 0 2 2 2
Each term divided by the leading coefficient 2 2 2
x2 + 4x - = 0 3 2
Move the constant to the right side. 3 2
+ +
Add the square of the middle term on both sides

5. Factor left side and simplify right side
Take square root on both sides
solve for x

6. Solve for x by completing square
1. x2 + 6x + 3 = 0
2. x2 – 4x – 6 = 0
3. x2 + 10x + 17 = 0