 #  Quadratic Equations Solve by Completing the Square.

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 Quadratic Equations Solve by Completing the Square

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

Help! Aim: Use completing the square in order to solve for x in a quadratic equation. Solve for x: x 2 + 4x – 56 = 0 try factoring (x )(x ) = 0 + ? try using the quadratic formula

What’s Up? Aim: Use completing the square in order to solve for x in a quadratic equation. What is the discriminant?x 2 + 4x – 56 = 0 b 2 – 4ac (4) 2 – 4(1)(-56) 16 + 224 240 Because the discriminant is positive, the root is. When a = 14 & b is an number, we can use a quicker method to solve for x! real 1 even

Completing the Square Aim: Use completing the square in order to solve for x in a quadratic equation. Solve for x: x 2 + 4x – 56 = 0 x 2 + 4x = 56 Make sure a = 1 Get only x’s to one side. ✓ Add on (½ b) 2 to both sides. x 2 + 4x + = 56 + 4 4 44 Write the perfect square. (x + 2) 2 = √(x + 2) 2 = √60 & square root both sides. √(x + 2) 2 = √60 Isolate the x. x + 2 = ±√60 x = -2 ± √60 x = -2 + 2 √15 x = -2 - 2 √15 b ≠ 0 ✓

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

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