Solve.

2

2

2

1. 5 13 6

2. 3 10 6

3. (x-2) 2 18

x x

x x

2

or 35

x x

4

or 23

x x

2or 6x x

Question of the Day

CCGPS GeometryDay 62 (10-24-13)

UNIT QUESTION: How are real life scenarios represented by quadratic functions?

Today’s Question:When is it useful to solve quadratics by completing the square?Standard: MCC9-12..A.REI.4b

Completing the Square

• Completing the square is used for all those not factorable problems!!

• It is used to solve these equations for the variable.

• It gets a little messy when a is not 1.

Perfect Square Trinomials

Examples x2 + 6x + 9 x2 - 10x + 25 x2 + 12x + 36

Creating a Perfect Square Trinomial

In the following perfect square trinomial, the constant term is missing. x2 + 14x + ____

Find the constant term by squaring half the coefficient of the linear term.

(14/2)2

x2 + 14x + 49

Perfect Square Trinomials

Create perfect square trinomials. x2 + 20x + ___ x2 - 4x + ___ x2 + 5x + ___

Example 1 Solving by Completing the Square

Solve the following equation by completing the square:

Step 1: Rewrite so all terms containing x are on one side.

2 8 20 0x x

2 8 20x x

Example 1 Continued

Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

2 8 =20 + x x

21( ) 4 then square it, 4 16

28

2 8 2016 16x x

Example 1 Continued

Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

2 8 2016 16x x

2

( 4)( 4) 36

( 4) 36

x x

x

Step 4: Take the square root of each side.

2( 4) 36x

( 4) 6x

Example 1 Continued

Step 5: Solve for x. 4 6

4 6 an

d 4 6

10 and 2 x=

x

x x

x

Example 2 Solving by Completing the Square

Solve the following equation by completing the square:

Step 1: Rewrite so all terms containing x are on one side.

2 6 18 0 x x

2 6 18 x x

Example 2 Continued

Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

2 6 =18 + x x

21( ) 3 then square it, (-36 ) 9

2

2 6 189 9 x x

Example 2 Continued

Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

2 6 189 9 x x

2

( 3)( 3) 27

( 3) 27

x x

x

Step 4: Take the square root of each side.

2( 3) 27 x

( 3) 3 3 x

Example 2 Continued

Step 5: Solve for x. 3 3 3 x

Solve each by Completing the Square

Solve each by Completing the Square

x2 + 4x – 4 = 0x2 – 2x – 1 = 0

Example 4 Finding Complex Solutions

x2 - 8x + 36 = 0 x2 +6x = - 34

Example 5 Solving When a≠0