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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.

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Quadratic Equations

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  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

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