英语词汇“to complete the square”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

Mathematics. to complete the square: to express a quadratic equation ax² + bx + c = 0 in the form aX² + C = 0, typically in order to solve it; (also) to construct a square with a given line as one side. Also in extended use.The conversion of the equation may be done by making X = x + b/2a, and C = c − b²/4a.The expression arises from a geometrical representation of the algebraic process. A square of side x is considered along with two rectangles each of sides x and b/2a. When the two rectangles are placed alongside adjacent faces of the square, it is seen that a small square of side b/2a is need to complete the larger square of side x + b/2a.

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1685 J. Wallis Treat. Algebra xxxii. 134 Whatever the Process be, whether this, by compleating the Square; or that before mentiones..the Result will be still the same.

1702 J. Harris New Short Treat. Algebra 57 Which is the Common Canon for Solving Equations by Compleating the Square.

1728 J. Raphson & S. Cunn tr. I. Newton Universal Arithmetick (ed. 2) 125 Complete the square ABCD, and bisect the Line EF in G.

1806 C. Hutton Course Math. (ed. 5) I. 247 The general method of solving quadratic equations, is by what is called completing the square.

1834 Treat. Pact. Geom. (Commissioners of National Educ., Ireland) 15 With the radius A B and C B, describe two arcs cutting each other at D; join D A and D C, which will complete the square.

1854 W. Minifie Text Bk. Geom. Drawing (ed. 5) i. 20 On a given line A. B to construct a square whose side shall be equal to the given line... 4th. Draw A. E, E. F and F. B, which complete the square.

1855 Pop. Educator VI. 528/1 The advantage of this method is, that it avoids the introduction of fractions in completing the square.

1897 Geogr. Jrnl. 9 213 The map has contained the whole of the counties of Worcester and Warwick, with as much of the adjoining shires as would complete the square.

1947 J. H. Jeans Growth of Physical Sci. ii. 32 This can be seen from the theorem of Pythagoras, or by completing the square on AC as in fig. 9.

1969 W. C. Elmore & M. A. Heald Physics of Waves xi. 406 By completing the square, show that the ‘moving’ coordinate system used in this section..eliminates the linear term, i.e., results in a pure quadratic phase exponent.

2007 M. J. Sterling Algebra II Workbk. for Dummies ii. 26 Here's how to solve the quadratic equation ax² + bx + c = 0 by completing the square.

单词	to complete the square
释义	> as lemmas to complete the square Mathematics. to complete the square: to express a quadratic equation ax² + bx + c = 0 in the form aX² + C = 0, typically in order to solve it; (also) to construct a square with a given line as one side. Also in extended use.The conversion of the equation may be done by making X = x + b/2a, and C = c − b²/4a.The expression arises from a geometrical representation of the algebraic process. A square of side x is considered along with two rectangles each of sides x and b/2a. When the two rectangles are placed alongside adjacent faces of the square, it is seen that a small square of side b/2a is need to complete the larger square of side x + b/2a. ΚΠ 1685 J. Wallis Treat. Algebra xxxii. 134 Whatever the Process be, whether this, by compleating the Square; or that before mentiones..the Result will be still the same. 1702 J. Harris New Short Treat. Algebra 57 Which is the Common Canon for Solving Equations by Compleating the Square. 1728 J. Raphson & S. Cunn tr. I. Newton Universal Arithmetick (ed. 2) 125 Complete the square ABCD, and bisect the Line EF in G. 1806 C. Hutton Course Math. (ed. 5) I. 247 The general method of solving quadratic equations, is by what is called completing the square. 1834 Treat. Pact. Geom. (Commissioners of National Educ., Ireland) 15 With the radius A B and C B, describe two arcs cutting each other at D; join D A and D C, which will complete the square. 1854 W. Minifie Text Bk. Geom. Drawing (ed. 5) i. 20 On a given line A. B to construct a square whose side shall be equal to the given line... 4th. Draw A. E, E. F and F. B, which complete the square. 1855 Pop. Educator VI. 528/1 The advantage of this method is, that it avoids the introduction of fractions in completing the square. 1897 Geogr. Jrnl. 9 213 The map has contained the whole of the counties of Worcester and Warwick, with as much of the adjoining shires as would complete the square. 1947 J. H. Jeans Growth of Physical Sci. ii. 32 This can be seen from the theorem of Pythagoras, or by completing the square on AC as in fig. 9. 1969 W. C. Elmore & M. A. Heald Physics of Waves xi. 406 By completing the square, show that the ‘moving’ coordinate system used in this section..eliminates the linear term, i.e., results in a pure quadratic phase exponent. 2007 M. J. Sterling Algebra II Workbk. for Dummies ii. 26 Here's how to solve the quadratic equation ax² + bx + c = 0 by completing the square. extracted from completev. < as lemmas
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