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  2. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    Given a quadratic polynomial of the form + + it is possible to factor out the coefficient a, and then complete the square for the resulting monic polynomial. Example: + + = [+ +] = [(+) +] = (+) + = (+) + This process of factoring out the coefficient a can further be simplified by only factorising it out of the first 2 terms.

  3. Solving quadratic equations with continued fractions - Wikipedia

    en.wikipedia.org/wiki/Solving_quadratic...

    The quadratic equation on a number can be solved using the well-known quadratic formula, which can be derived by completing the square. That formula always gives the roots of the quadratic equation, but the solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic fraction that can be evaluated ...

  4. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    Figure 1. Plots of quadratic function y = ax 2 + bx + c, varying each coefficient separately while the other coefficients are fixed (at values a = 1, b = 0, c = 0). A quadratic equation whose coefficients are real numbers can have either zero, one, or two distinct real-valued solutions, also called roots.

  5. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    A similar but more complicated method works for cubic equations, which have three resolvents and a quadratic equation (the "resolving polynomial") relating ⁠ ⁠ and ⁠ ⁠, which one can solve by the quadratic equation, and similarly for a quartic equation (degree 4), whose resolving polynomial is a cubic, which can in turn be solved. [14]

  6. Horner's method - Wikipedia

    en.wikipedia.org/wiki/Horner's_method

    With a Supplement, Containing Two Other Methods of Solving Equations, Derived from the Same Principle (PDF). Richard Watts. Archived from the original (PDF) on 2014-01-06 Holdred's method is in the supplement following page numbered 45 (which is the 52nd page of the pdf version). Horner, William George (July 1819). "A new method of solving ...

  7. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    The quadratic formula, which concisely expresses the solutions of all quadratic equations The Rubik's Cube group is a concrete application of group theory. [ 26 ] Algebra is the art of manipulating equations and formulas.

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