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Published byDaniel Grant Modified over 6 years ago

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2.4 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square

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**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

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**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

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

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**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 (Next week’s lesson)

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**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 = )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

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**Solve by Completing the Square**

+9

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**Solve by Completing the Square**

+121

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**Solve by Completing the Square**

+1

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**Solve by Completing the Square**

+25

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**Solve by Completing the Square**

+16

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**Solve by Completing the Square**

+9

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**The coefficient of x2 must be “1”**

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**The coefficient of x2 must be “1”**

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