“completing the square”的概念、定义、翻译、参考文献-科学参考

completing the square

Mathematics

单词	completing the square
释义	completing the square Mathematics The quadratic equation 2x² + 5x + 1 = 0 can be solved by first writing it as $x^{2} + \frac{5}{2} x = - \frac{1}{2},$ and then ${(x + \frac{5}{4})}^{2} = - \frac{1}{2} + \frac{25}{16} = \frac{17}{16} .$ This step is known as completing the square: the left-hand side is made into an exact square by adding a suitable constant to both sides. The solutions for x can then be arrived at by taking square roots and rearranging. Applying this method to the general quadratic equation derives the quadratic formula.
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