 # 8-1 Completing the Square

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8-1 Completing the Square
Solving Quadratic Equations by Factoring: Set the equation equal to 0 Factor Set each factor = 0 and solve Example 1a: Example 1b: Solve x2 = Solve p2 = 64

8-1 Completing the Square
Example 2a: Solve 6x2 – 7x – 3 = 0 Example 2b: Solve 6m2 – 5m + 1 = 0

8-1 Completing the Square
Square Root Property: If c > 0, the equation x2 = c has TWO solutions: x = or x = – (Use when there is an x2 term and another number) Move constant over to other side Find the square root of both sides Use the square root property to find the answers Example 3a: Solve: x2 – 12 = 0

8-1 Completing the Square
Square Root Property: Example 3b: Solve x2 – 18 = 0

8-1 Completing the Square
Square Root Property: Example 4a: (x – 3)2 = 16 Problem #31: (x + 5)2 – 3 = 0

8-1 Completing the Square
Example 7: Add a number to make each binomial a perfect square: x2 + 10x x2 – 6x Steps Find ½ of the coefficient of the x term Square it Add it the equation

8-1 Completing the Square
When the coefficient of x is 1: If necessary, move the number to other side of the equation to put it on the right side of the equal sign. Complete the square: Find ½ of the coefficient of the x term and square it. Add the square to both sides of the equation. Factor the trinomial square on the left. Solve the resulting equation using the square root property.

8-1 Completing the Square
Example 8a: Use completing the square to solve: x2 + 8x + 7 = 0

8-1 Completing the Square
Example 8b: Use completing the square to solve: a2 + 5a + 4 = 0

8-1 Completing the Square
Homework: Pg 519 #10, 12, 16, 18, 24, 26, 28, 30, 32, 34 Pg 519 #44, 46, 48, 48, 68, 74