Your SlideShare is downloading. ×
0
Solving Quadratics by Completing the Square
Solving Quadratics by Completing the Square
Solving Quadratics by Completing the Square
Solving Quadratics by Completing the Square
Solving Quadratics by Completing the Square
Solving Quadratics by Completing the Square
Solving Quadratics by Completing the Square
Solving Quadratics by Completing the Square
Solving Quadratics by Completing the Square
Solving Quadratics by Completing the Square
Solving Quadratics by Completing the Square
Solving Quadratics by Completing the Square
Solving Quadratics by Completing the Square
Solving Quadratics by Completing the Square
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Solving Quadratics by Completing the Square

290

Published on

Published in: Education, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
290
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
19
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. Solving Quadratic Equations by Completing the Square
  • 2. Perfect Square Trinomials Examples x2 + 6x + 9 x2 - 10x + 25 x2 + 12x + 36
  • 3. 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
  • 4. Perfect Square Trinomials Create perfect square trinomials. x2 + 20x + ___ x2 - 4x + ___ x2 + 5x + ___ 100 4 25/4
  • 5. Solving Quadratic Equations by Completing the Square Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation x + 8 x − 20 = 0 2 x + 8 x = 20 2
  • 6. Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. x + 8x + 2 W=20 +W 1 • (8) = 4 then square it, 42 = 16 2 x + 8 x + 16 = 20 + 16 2
  • 7. Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation. x + 8 x + 16 = 20 + 16 2 ( x − 4)( x − 4) = 36 ( x − 4) = 36 2
  • 8. Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side ( x + 4) = 36 2 ( x + 4) = ±6
  • 9. Solving Quadratic Equations by Completing the Square Step 5: Set up the two possibilities and solve x = −4 ± 6 x = −4 − 6 and x = −4 + 6 x = −10 and x=2
  • 10. Completing the Square-Example #2 Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation, the constant to the right side of the equation. 2 x − 7 x + 12 = 0 2 2 x − 7 x = −12 2
  • 11. Solving Quadratic Equations by Completing the Square 2x − 7x + W =-12 +W Step 2: Find the term 2x 7x 12 that completes the square − + W= − + W on the left side of the 2 2 2 2 2 equation. Add that term to both sides. The quadratic coefficient must be equal to 1 before you complete the square, so you must divide all terms by the quadratic coefficient first. 7 x − x +W −6 +W = 2 2 1 7 7 • ( ) = then square it, 2 2 4 7 49 49 x − x+ = −6 + 2 16 16 2 2 49 7  ÷ =  4  16
  • 12. Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation. 7 49 49 x − x+ = −6 + 2 16 16 2 2 7 96 49  x− ÷ =− + 4 16 16  2 7 47  x− ÷ =− 4 16 
  • 13. Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side 7 2 −47 (x − ) = 4 16 7 −47 (x − ) = ± 4 4 7 i 47 x= ± 4 4 7 ± i 47 x= 4
  • 14. Solving Quadratic Equations by Completing the Square Try the following examples. Do your work on your paper and then check your answers. 1. x + 2 x − 63 = 0 2 2. x + 8 x −84 = 0 2 3. x − 5 x − 24 = 0 2 4. x + 7 x +13 = 0 2 5. 3 x 2 +5 x + 6 = 0 1. ( −9, 7 ) 2.(6, −14) 3. ( −3,8 )  −7 ± i 3  4.  ÷  ÷ 2    −5 ± i 47  5.  ÷  ÷ 6  

×