Chapter 8.8(b) completing the square.notebook
March 22, 2017
Homework Questions???
Bellwork:
Complete the Square:
1) x2 + 8x + ___
2) x2 ­ 5x + ____
Solve:
2
64
3) (x + 6) = 2
/81
4) (x ­ 4) = 23
5) Find the equation of the line: Mar 12­10:35 AM
Mar 30­10:42 AM
Solve by Completing the Square: x2 + 5x = 8
Step 1: ax2 + bx = c
Chapter 8.8(b) Completing the Square
Solve quadratic equations by completing the square. Be able to complete the square in the form ax2 + bx = c.
Step 2: b/2
Step 3: (b/2)2
Step 4: Add (b/2)2 Step 5: Factor Solving:
Step 6: Square Root
Step 7: Solve for x
Mar 12­10:40 AM
Steps for completing the square: 5x2 ­ 21 = 10x
Step 1: Rearrange equation into the form ax2 + bx = c
5x2 ­21 = 10x
­10x ­10x
5x2 ­ 10x ­ 21 = 0
+21 +21
2
5x ­ 10x = 21
5 5
Part b: If a ≠ 1, then factor it out a(x2 + bx) = c
5(x2 ­ 2x) = 21
Mar 21­10:00 AM
example:
Steps for completing the square: 4x2 ­ 65 = ­16v
Step 1: ax2 + bx = c
Part b: If a ≠ 1, then a(x2 + bx) = c
Step 2: b/2
Step 2: Take b and divide by 2, and simplify if possible: b/2
­2
/2 = ­1
Step 3: Square what you got in the last step (b/2)2
Step 3: (b/2)2
Step 4: Add (b/2)2 (­1)2 = 1
Step 4: Add (b/2)2 to both sides of the equation:
Part b: multiply (b/2)2 by a.
2
5(x ­ 2x + 1) = 21 + 1
Part b: If you factored out an a, multiply (b/2)2 by a.
Step 5: Factor 2
5(x ­ 2x + 1) = 21 + 1 5
5(x2 ­ 2x + 1) = 21 + 5
5(x2 ­ 2x + 1) = 26
Step 5: Factor the left side (perfect square trinomial)
5(x2 ­ 2x + 1) = 26
5(x ­ 1)(x ­ 1) = 26
5(x ­ 1)2 = 26
Mar 12­10:43 AM
Mar 12­2:07 PM
1
Chapter 8.8(b) completing the square.notebook
Solve by completing the square: 2x2 + 12x + 10 = 0
Step 1: ax2 + bx = c
2x2 + 12x = ­10
Part b: factor a out a(x2 + bx) = c 2(x2 + 6x) = ­10
March 22, 2017
Example:
Solve by completing the square: 4x2 + 8x ­ 2 = 4
Step 1: ax2 + bx = c
Step 2: b/2
b/2 = (6) ÷ 2 = 3
Step 3: Square what you got in the last step (b/2)2
(3)2 = 9
Step 4: Add (b/2)2 to both sides of the equation
Part b: If you factored out an a, multiply (b/2)2 by a.
2(x2 + 6x + 9) = ­10 + 9(2)
2(x2 + 6x + 9) = ­10 + 18
2(x2 + 6x + 9) = 8
Part b: If a ≠ 1, then a(x2 + bx) = c
Step 2: b/2
Step 3: (b/2)2
Step 4: Add (b/2)2 Step 5: Factor the left side (perfect square trinomial)
2(x + 3)2 = 8
Step 6: Solve
Divide each side by a
2(x + 3)2 = 8
2
2
(x + 3)2 = 4
Take the square root of each side
(x + 3) = ± 2
Part b: multiply (b/2)2 by a.
Step 5: Factor
Solve:
Step 6: Divide by a
Step 7: square root
add/subtract (b/2)
x + 3 = 2
x + 3 = ­2
­3 ­3
­3 ­3
x = ­1, ­5
Step 8: solve
Mar 12­10:44 AM
Solve by completing the square: 5x2 ­ 10x ­ 19 = ­4
Mar 12­2:06 PM
Solve by completing the square: 2x2 ­ 7x ­ 29 = 10
Step 1: ax2 + bx = c
2x2 ­ 7x = 39
2
2
Part b: factor a out a(x + bx) = c 2
Step 1: ax + bx = c
2(x ­ 7
/2x) = 39
Step 2: b/2
7
7
b/2 = (­ /2) ÷ 2 = (­ /2)(½) = ­7/4
Part b: If a ≠ 1, then a(x2 + bx) = c
Step 3: Square what you got in the last step (b/2)2
(­7/4)2 = 49/16
Step 2: b/2
Step 4: Add (b/2)2 to both sides of the equation
Part b: If you factored out an a, multiply (b/2)2 by a.
2(x2 ­ 7/2x + 49/16) = 39/1 + (49/16)(2/1)
2(x2 ­ 7/2x + 49/16) = 361/8
Step 3: (b/2)2
Step 5: Factor the left side (perfect square trinomial)
Step 4: Add (b/2)2 :
7
2
361
2(x ­ /4) = 2
Part b: multiply (b/2) by a.
Step 5: Factor /8
Step 6: Solve
Divide each side by a
2(x ­ 7/4)2 = 361/8
2
2
(x ­ 7/4)2 = (361/8)(½) = 361/16
Solve:
Step 6: Divide by a
Take the square root of each side
(x ­ 7/4)2 = 361/16
x ­ 7/4 = ± 19/4
add/subtract (b/2)
x ­ 7/4 = ± 19/4
+7/4 +7/4
Step 7:square root
Step 8: solve
x = 7/4 + 19/4 or x = 7/4 ­ 19/4
x = 13/2 or x = ­3
Mar 12­2:08 PM
Mar 12­10:44 AM
Example:
Solve by completing the square: 5x2 ­ 2x ­ 12 = 0
Step 1: ax2 + bx = c
Part b: If a ≠ 1, then a(x2 + bx) = c
Step 2: b/2
Step 3: (b/2)2
Step 4: Add (b/2)2 What would the next step be to complete the square?
4x2 ­ 16x ­ 78 = 0
+78 +78
4x2 ­ 16x = 78
2
4(x ­ 4x) = 78
b = ­4, b/2 = ­2
(b/2)2 = (­2)2 = 4
Part b: multiply (b/2)2 by a.
Step 5: Factor
Solve:
Step 6: Divide by a
Step 7: square root
Step 8: solve
Mar 21­10:10 AM
Mar 12­2:15 PM
2
Chapter 8.8(b) completing the square.notebook
March 22, 2017
Homework
Completing the Square #13­20
Mar 12­2:15 PM
Mar 22­4:10 PM
3