Quadratic Equation by Completing Sq.ppt

Solving Quadratic Equation by Completing the Square

1. Do Now
 Factor the expression.
1.x
2
+ 18x + 81
1.x
2
- 22x + 121

2. Completing the
Square
OBJECTIVE:
SOLVE QUADRATIC EQUATIONS BY COMPLETING THE
SQUARE

3. Completing the Square
Find the value of c that makes x
2
- 6x + c a
perfect square trinomial. Then write the
expression as the square of a binomial.
To find the value of c, use the “b” value
(ax
2
+bx+c):
1. Find half the coefficient of x.
2. Square the result of Step 1.
3. Replace c with the result of Step 2.
Answer:when when cc = 9, = 9, xx
22
– 6 – 6xx + 9 = ( + 9 = (xx – 3) – 3)
22
xx
22
– 6 – 6xx + 9 + 9
(– 3)(– 3)
2 2
= =
½ (– 6)½ (– 6)

= =

4. Example: Completing the Square
Find the value of c that makes x
2
- 12x + c a
perfect square trinomial. Then write the
expression as the square of a binomial.
To find the value of c, use the “b” value
(ax
2
+bx+c):
1. Find half the coefficient of x.
2. Square the result of Step 1.
3. Replace c with the result of Step 2.
Answer:

5. Practice
Find the value of c that makes the expression a
perfect square trinomial. Then write the
expression as the square of a binomial.
3. x
2
- 10x + c
4. x
2
+ 18x + c

6. Solving Quadratics

7. Example

8. Solve the equation by
completing the square.
1. x
2
+ 2x – 3 = 0
2. x
2
- 6x + 16 = 0

9. Solve the equation by
completing the square.
3. x
2
- 8x - 20 = 0
4. x
2
+ 4x - 15 = 21

10. Solve the equation by
completing the square.
5. x
2
- 2x - 2 = 0
6. x
2
+ 6x + 3 = 0