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  2. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    Animation depicting the process of completing the square. ( Details , animated GIF version ) In elementary algebra , completing the square is a technique for converting a quadratic polynomial of the form ⁠ a x 2 + b x + c {\displaystyle \textstyle ax^{2}+bx+c} ⁠ to the form ⁠ a ( x − h ) 2 + k {\displaystyle \textstyle a(x-h)^{2}+k ...

  3. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    This method for completing the square is ancient and was known to the 8th–9th century Indian mathematician Śrīdhara. [12] Compared with the modern standard method for completing the square, this alternate method avoids fractions until the last step and hence does not require a rearrangement after step 3 to obtain a common denominator in the ...

  4. Replica trick - Wikipedia

    en.wikipedia.org/wiki/Replica_trick

    a standard Gaussian integral which can be easily computed (e.g. completing the square). To calculate the free energy, we use the replica trick: ln ⁡ Z = lim n → 0 Z n − 1 n {\displaystyle \ln Z=\lim _{n\to 0}{\dfrac {Z^{n}-1}{n}}} which reduces the complicated task of averaging the logarithm to solving a relatively simple Gaussian ...

  5. Parent function - Wikipedia

    en.wikipedia.org/wiki/Parent_function

    In mathematics education, a parent function is the core representation of a function type without manipulations such as translation and dilation. [1] For example, for the family of quadratic functions having the general form

  6. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    This "completes the square", converting the left side into a perfect square. Write the left side as a square and simplify the right side if necessary. Produce two linear equations by equating the square root of the left side with the positive and negative square roots of the right side. Solve each of the two linear equations.

  7. Large meals after 5 pm could contribute to type 2 diabetes risk

    www.aol.com/large-meals-5-pm-could-140000242.html

    Consuming more than 45% of daily calories after 5 p.m. can contribute to greater risk of type 2 diabetes, cardiovascular problems, and chronic inflammation, a recent study suggests.

  8. Donald Trump Slams Those Who Are Defending Luigi Mangione ...

    www.aol.com/donald-trump-slams-those-defending...

    Donald Trump is condemning the alleged actions of Luigi Mangione and the people who defend him.. In a Dec. 17 news conference, the president-elect, 78, denounced the man accused of killing ...

  9. Factorization - Wikipedia

    en.wikipedia.org/wiki/Factorization

    A typical use of this is the completing the square method for getting the quadratic formula. Another example is the factorization of x 4 + 1. {\displaystyle x^{4}+1.} If one introduces the non-real square root of –1 , commonly denoted i , then one has a difference of squares x 4 + 1 = ( x 2 + i ) ( x 2 − i ) . {\displaystyle x^{4}+1=(x^{2 ...

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