Algebra 1 Jarrett Sutter 10.5 Completing the Square Algebra 1 Jarrett Sutter

Ways to Solve a Quadratic Factor Split the Middle Grouping Factoring a monomial out If a quadratic equation does not factor we can solve it by two different methods 1.) Completing the Square (today’s lesson) 2.) Quadratic Formula (Thursday) That leaves us 5 ways to solve. There are a lot of ways to get your answer. Don’t give up.

Steps to complete the square 1.) You will get an expression that looks like this: AX²+ BX 2.) Our goal is to make a square such that we have (a + b)² = a² +2ab + b² 3.) We take ½ of the X coefficient (Divide the number in front of the X by 2) 4.) Then square that number

To Complete the Square x2 + 6x 3 Take half of the coefficient of ‘x’ Square it and add it 9 x2 + 6x + 9 = (x + 3)2

Complete the square, and show what the perfect square is:

Steps to solve by completing the square 1.) If the quadratic does not factor, move the constant to the other side of the equation Ex: x²-4x -7 =0 x²-4x=7 2.) Work with the x²+ x side of the equation and complete the square by taking ½ of the coefficient of x and squaring Ex. x² -4x 4/2= 2²=4 3.) Add the number you got to complete the square to both sides of the equation Ex: x² -4x +4 = 7 +4 4.)Simplify your trinomial square Ex: (x-2)² =11 5.)Take the square root of both sides of the equation Ex: x-2 =±√11 6.) Solve for x Ex: x=2±√11

Solve by Completing the Square +9

Solve by Completing the Square +121

Solve by Completing the Square +1

Solve by Completing the Square +25

Solve by Completing the Square +16

Solve by Completing the Square +9

The coefficient of x2 must be “1”

The coefficient of x2 must be “1”

Solving Quadratic Equations by Completing the Square Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation

Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

Solving Quadratic Equations by Completing the Square Step 5: Set up the two possibilities and solve