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First, add (or subtract) to place the constant on the right side.

Quadratic Equation: Solving by completing the square . Example: Solve 3 x 2 + 12 x + 7 = 0. First, add (or subtract) to place the constant on the right side. 3 x 2 + 12 x = - 7. Next, divide every term on both sides by a number chosen to make "1" the coefficient of the x 2 .

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First, add (or subtract) to place the constant on the right side.

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  1. Quadratic Equation: Solving by completing the square Example: Solve 3x2 + 12x + 7 = 0. First, add (or subtract) to place the constant on the right side. 3x2 + 12x = - 7 Next, divide every term on both sides by a number chosen to make "1" the coefficient of the x2. Next, take half of the x-term coefficient and square this. Then add this to both sides. Half of 4 is 2. Square this to get 4 so:

  2. Quadratic Equation: Solving by completing the square The trinomial on the left is a perfect square. It can be written in the form: (x + half of the x-term coef.)2. Note, the constant terms on the right can be combined now. Now solve by taking the square root of both sides. Slide 2

  3. The solutions are Notes: The example on the preceding two slides resulted in two real solutions. Most textbooks would display the solutions as (merged into a single fraction). However, when the solutions are nonreal (as in one just tried) the solutions are usually written in the standard form of a complex number, a + bi. Quadratic Equation: Solving by completing the square Try to solve 2x2 – 6x = - 7 by completing the square. Slide 3

  4. Quadratic Equation: Solving by completing the square END OF PRESENTATION Click to rerun the slideshow.

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