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  2. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    For example, the equation x + y = 2x – 1 is solved for the unknown x by the expression x = y + 1, because substituting y + 1 for x in the equation results in (y + 1) + y = 2(y + 1) – 1, a true statement. It is also possible to take the variable y to be the unknown, and then the equation is solved by y = x – 1.

  3. System of polynomial equations - Wikipedia

    en.wikipedia.org/wiki/System_of_polynomial_equations

    Bézout's theorem asserts that a well-behaved system whose equations have degrees d 1, ..., d n has at most d 1 ⋅⋅⋅d n solutions. This bound is sharp. If all the degrees are equal to d, this bound becomes d n and is exponential in the number of variables. (The fundamental theorem of algebra is the special case n = 1.)

  4. Elementary algebra - Wikipedia

    en.wikipedia.org/wiki/Elementary_algebra

    has no real number solution since no real number squared equals −1. Sometimes a quadratic equation has a root of multiplicity 2, such as: (+) = For this equation, −1 is a root of multiplicity 2. This means −1 appears twice, since the equation can be rewritten in factored form as

  5. Polynomial - Wikipedia

    en.wikipedia.org/wiki/Polynomial

    For example, antiderivatives of x 2 + 1 have the form ⁠ 1 / 3 ⁠ x 3 + x + c. For polynomials whose coefficients come from more abstract settings (for example, if the coefficients are integers modulo some prime number p , or elements of an arbitrary ring), the formula for the derivative can still be interpreted formally, with the coefficient ...

  6. 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]

  7. List of nonlinear ordinary differential equations - Wikipedia

    en.wikipedia.org/wiki/List_of_nonlinear_ordinary...

    Nonlinear ones are of particular interest for their commonality in describing real-world systems and how much more difficult they are to solve compared to linear differential equations. This list presents nonlinear ordinary differential equations that have been named, sorted by area of interest.

  8. California veteran Jerry Heath, who waited months for $44.3M ...

    www.aol.com/california-veteran-jerry-heath...

    A US Army vet and retired police detective who said that the California lottery was taking too long to pay out his jaw-dropping $44.3 million jackpot has finally claimed his winnings after months ...

  9. Slutsky equation - Wikipedia

    en.wikipedia.org/wiki/Slutsky_equation

    The first term on the right-hand side represents the substitution effect, and the second term represents the income effect. [1] Note that since utility is not observable, the substitution effect is not directly observable, but it can be calculated by reference to the other two terms in the Slutsky equation, which are observable.