1 / 7

Quadratic Equations

Quadratic Equations. Solve by Completing the Square. Aim: Use completing the square in order to solve for x in a quadratic equation. Remember:. Solve for x :. Aim: Use completing the square in order to solve for x in a quadratic equation. Help!. Solve for x: x 2 + 4 x – 56 = 0.

zaide
Download Presentation

Quadratic Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Quadratic Equations Solve by Completing the Square

  2. Aim: Use completing the square in order to solve for x in a quadratic equation. Remember: Solve for x:

  3. Aim: Use completing the square in order to solve for x in a quadratic equation. Help! Solve for x: x2 + 4x – 56 = 0 (x )(x ) = 0 try factoring + ? + ? try using the quadratic formula That’s a lot of work!

  4. Aim: Use completing the square in order to solve for x in a quadratic equation. What’s Up? 1 4 What is the discriminant? x2 + 4x – 56 = 0 b2 – 4ac (4)2 – 4(1)(-56) 16 + 224 240 Because the discriminant is positive, the root is . real even 1 & b is an number, When a = we can use a quicker method to solve for x!

  5. Aim: Use completing the square in order to solve for x in a quadratic equation. Completing the Square Solve for x: x2 + 4x – 56 = 0 Make sure a = 1 ✓ ✓ b ≠0 x2 + 4x = 56 Get only x’s to one side. x2 + 4x + = 56 + Add on (½ b)2 to both sides. 4 4 4 4 Write the perfect square. √(x + 2)2= √60 (x + 2)2= & square root both sides. x + 2= ±√60 x= -2 ± √60 x= -2 + 2 √15 x= -2 - 2 √15 Isolate the x. √(x + 2)2= √60

  6. Try … Solve for the following by completing the square: 1. x2 - 12x – 10 = 0 2. x2 - 4x + 57 = -5 x2 - 12x = 10 x2 - 4x = -62 x2 - 12x += 10 + x2 - 4x += -62 + 36 36 36 4 4 36 4 4 √(x – 2)2 = √ √(x – 2)2 = √-58 √(x – 6)2 = √ √(x – 6)2 = √46 √(x – 6)2 = √ √(x – 6)2 = √46 x – 2= ±√-58 x – 6= ±√46 √(x – 2)2 = √-58 x= 2 ± i√58 x= 2 + i√58 x= 2 - i√58 x= 6 ± √46 x= 6 - √46 x= 6 + √46

  7. Challenge Solve for the following by completing the square: √(x + 1)2 = √4 6x2 = -12x + 18 6 6 x2= -2x + 3 x2 + 2x = 3 x2 + 2x += 3 + 1 1 1 1 √(x – 6)2 = √ √(x + 1)2 = √4 x + 1= ± 2 x= -1 ± 2 x= 1 x= -3

More Related