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13.3 Completing the Square

13.3 Completing the Square. Objective: To complete a square for a quadratic equation and solve by completing the square. Steps to complete the square. 1.) You will get an expression that looks like this: AX ²+ BX 2.) Our goal is to make a square such that we have (a + b)² = a² +2ab + b²

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13.3 Completing the Square

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  1. 13.3 Completing the Square • Objective: To complete a square for a quadratic equation and solve by completing the square

  2. 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

  3. To Complete the Squarex2 + 6x 3 9 • Take half of the coefficient of ‘x’ • Square it and add it x2 + 6x + 9 = (x + 3)2

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

  5. To solve by completing the square • 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 (Monday’s lesson)

  6. 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

  7. +9 +9 Solve by Completing the Square

  8. +121 +121 Solve by Completing the Square

  9. +1 +1 Solve by Completing the Square

  10. +25 +25 Solve by Completing the Square

  11. +16 +16 Solve by Completing the Square

  12. +9 +9 Solve by Completing the Square

  13. The coefficient of x2 must be “1”

  14. The coefficient of x2 must be “1”

  15. AssignmentPage 588(2-32) even

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