8-1 Completing the SquareSolving Quadratic Equations by

Factoring:Set the equation equal to 0FactorSet each factor = 0 and solve

Example 1a: Example 1b:Solve x2 = 9 Solve p2 = 64

8-1 Completing the SquareExample 2a: Solve 6x2 – 7x – 3 = 0

Example 2b: Solve 6m2 – 5m + 1 = 0

8-1 Completing the SquareSquare 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 sideFind the square root of both sidesUse the square root property to find the answers

Example 3a: Solve: x2 – 12 = 0

c c

8-1 Completing the SquareSquare Root Property:

Example 3b: Solve x2 – 18 = 0

8-1 Completing the SquareSquare Root Property:

Example 4a: (x – 3)2 = 16

Problem #31: (x + 5)2 – 3 = 0

8-1 Completing the SquareExample 7: Add a number to make each binomial a perfect square:

1. x2 + 10x2. x2 – 6x

StepsFind ½ of the coefficient of the x termSquare itAdd it the equation

8-1 Completing the SquareCompleting the SquareWhen the coefficient of x is 1:1. If necessary, move the number to other

side of the equation to put it on the right side of the equal sign.

2. Complete the square:a) Find ½ of the coefficient of the x term and

square it.b) Add the square to both sides of the equation.

3. Factor the trinomial square on the left. 4. Solve the resulting equation using the

square root property.

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

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

8-1 Completing the SquareHomework:

Pg 519 #10, 12, 16, 18, 24, 26, 28, 30, 32, 34

Pg 519 #44, 46, 48, 48, 68, 74