About: Proof of the Quadratic formula   Sponge Permalink

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The Quadratic Formula used to solve equations of the form . It is: * Proof: Dividing our quadratic equation by (which is allowed because is non-zero), we have which is equivalent to The equation is now in a form in which we can conveniently complete the square. To "complete the square" is to add a constant (i.e., in this case, a quantity that does not depend on ) to the expression to the left of "", that will make it a perfect square trinomial of the form . Since in this case is , we must have , so we add the square of to both sides, getting Taking square roots of both sides yields

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  • Proof of the Quadratic formula
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  • The Quadratic Formula used to solve equations of the form . It is: * Proof: Dividing our quadratic equation by (which is allowed because is non-zero), we have which is equivalent to The equation is now in a form in which we can conveniently complete the square. To "complete the square" is to add a constant (i.e., in this case, a quantity that does not depend on ) to the expression to the left of "", that will make it a perfect square trinomial of the form . Since in this case is , we must have , so we add the square of to both sides, getting Taking square roots of both sides yields
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abstract
  • The Quadratic Formula used to solve equations of the form . It is: * Proof: Dividing our quadratic equation by (which is allowed because is non-zero), we have which is equivalent to The equation is now in a form in which we can conveniently complete the square. To "complete the square" is to add a constant (i.e., in this case, a quantity that does not depend on ) to the expression to the left of "", that will make it a perfect square trinomial of the form . Since in this case is , we must have , so we add the square of to both sides, getting The left side is now a perfect square; it is the square of . The right side can be written as a single fraction; the common denominator is . We get Taking square roots of both sides yields Subtracting from both sides, we get
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