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" If, then, any problem furnishes an equation in which the known term is negative, and greater than the square of half the coefficient of the first power of the unknown quantity, we infer, that the conditions of the problem are incompatible with each other. "
Ray's Algebra, Part First: On the Analytic and Inductive Methods of ... - Page 217
by Joseph Ray - 1848 - 240 pages
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The Popular Educator, Volumes 5-6; Volume 14

Geography - 1867 - 878 pages
...the first term. From this principle is derived the following METHOD FOB COMPLETING THE SQUARE. Take the square of half the co-efficient of the first power of the unknown quantity, and add it to both tides of the equation. It will be observed that there is nothing peculiar in the...
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Elements of Algebra: To which is Prefixed, a Choice Collection of ...

John Mole - Algebra - 1788 - 346 pages
...Queftion, CAS g CASE VI. When an Equation is prepared for completing the Square if the known Term be negative, and greater than the Square of half the Co-efficient of the fecond Term, then the Roots will be imaginary or impoffible : for EXAMPLE 1 Suppofe *•* — 6ax—...
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The British Encyclopedia, Or Dictionary of Arts and Sciences ..., Volume 1

William Nicholson - Natural history - 1809 - 716 pages
...all the terms, that the equation may be reduced to this farm, x* ^ px = i J. Then add to both sides the square of half the co-efficient of the first power of the unkwown quantity, by which means the first side of the equation is made a complete square, and the...
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volume 1

William Nicholson - Arts - 1819 - 432 pages
...all the terms, that the equation may be reduced to this form, x' ±px = ± g. Then add to both sides the square of half the co-efficient of the first power of the unknown quantity, by which means the first side 6f the equation is made a complete square, and the other consists of...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1820 - 352 pages
...derived the following rule : 305. To COMPLETE THE SQUARE, in an affected quadratic equation ; TAKE THE SQUARE OF HALF THE CO-EFFICIENT OF THE FIRST POWER OF THE UNKNOWN QUANTITY, AND ADD IT TO. BOTH SIDES OF THE EQUATION. Before completing the square, the known and unknown quantities...
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The North American Review, Volume 13

North American review and miscellaneous journal - 1821 - 526 pages
...the roots being imaginary in an equation, of which the known term is negative in the second member, and greater than the square of half the coefficient of the first power of the unknown quantity, he gives a striking specimen of his way of investigating ' analytical facts,' and displaying the spirit...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 570 pages
...what reason, when the known term of an equation of the second degree is negative in the second member, and greater than the square of half the coefficient of the first power of the unknown quantity, this equation can have only imaginary roots. 115. The expressions > V'"^, a + \s~-bi and, in general,...
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Elements of Algebra

Silvestre François Lacroix - Algebra - 1825 - 294 pages
...what reason, when the known term of an equation of the second degree is negative in the second member, and greater than the square of half the coefficient of the first power of the unknown quantity, this equation can have only imaginary roots. 1 1 5. The expressions and, in general, those, which involve...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1827 - 352 pages
...is derived the following rule: 305. To COMPLETE THE SQUARE, in an affected quadratic equation ; TAKE THE SQUARE OF HALF THE CO-EFFICIENT OF THE FIRST POWER OF THE UNKNOWN QUANTITY, AND ADD IT TO BOTH SIDES OF THE EQUATION. Before completing the square, the known and unknown quantities...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...square of that quantity in another term. To complete the square of an affected quadratic equation, take the square of half the co-efficient of the first power of the unknown quantity, and add it to both sides of the equation. After the square is completed, the equation is reduced, by...
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