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Deriving the Quadratic Formula

Deriving the Quadratic Formula. Use the complete the square method: Step one divide through by “a ”. Then isolate the terms with x (move everything else to the other side of the equal sign).

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Deriving the Quadratic Formula

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  1. Deriving the Quadratic Formula

  2. Use the complete the square method: Step one divide through by “a”

  3. Then isolate the terms with x (move everything else to the other side of the equal sign)

  4. Then “complete the square” by taking half of the coefficient of x and then squaring it and add it to both sides of the equation:

  5. Combine Information on Right Side • In order to combine the information on the right of this equals sign we need to have a common denominator. The common denominator will be 4a2 so we will have to multiply the numerator and the denominator of c/a by 4a.

  6. Multiply the numerator and the denominator of c/a by 4a.

  7. On the left of the equals sign of this equation is a perfect square so we can rewrite it as x + half of the coefficient of x)2.

  8. Since we are solving for x and x is being squared we now need to take the square root of both sides:

  9. We broke the denominator (4a2)out under its own square root since it is a perfect square and we can take the square root of it and write it as 2a

  10. We now need to isolate x:

  11. Since we already have a common denominator we can combine these terms and arrive at the quadratic formula

  12. Resources: • https://www.cdli.ca/learning-resources/mlos/mathematics-tutorials/unit-13.html

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