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To complete the square, form a squared binomial on the left-hand side of a quadratic equation, from which the solution can be found by taking the square root of both sides. The standard way to derive the quadratic formula is to apply the method of completing the square to the generic quadratic equation a x 2 + b x + c = 0 {\displaystyle ...
For the quadratic function y = x 2 − x − 2, the points where the graph crosses the x-axis, x = −1 and x = 2, are the solutions of the quadratic equation x 2 − x − 2 = 0. The process of completing the square makes use of the algebraic identity x 2 + 2 h x + h 2 = ( x + h ) 2 , {\displaystyle x^{2}+2hx+h^{2}=(x+h)^{2},} which represents ...
For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1) 2 = x 2 + 2x + 1. One of the important properties of squaring, for numbers as well as in many other mathematical systems, is that (for all numbers x), the square of x is the same as the square of its additive inverse −x.
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"x^y = y^x - commuting powers". Arithmetical and Analytical Puzzles. Torsten Sillke. Archived from the original on 2015-12-28. dborkovitz (2012-01-29). "Parametric Graph of x^y=y^x". GeoGebra. OEIS sequence A073084 (Decimal expansion of −x, where x is the negative solution to the equation 2^x = x^2)