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Bøker Bok 110 av 45Therefore, in the third and fourth forms, when q is greater than p2, that is, when...
" Therefore, in the third and fourth forms, when q is greater than p2, that is, when the known term is negative, and greater than the square of half the coefficient of the first power of x, both values of the unknown quantity are impossible. "
Elements of Algebra - Side 122
av Silvestre François Lacroix - 1825 - 276 sider
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The popular educator, Volumer 5-6

Popular educator - 1767
...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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The British Encyclopedia, Or Dictionary of Arts and Sciences ..., Volum 1

William Nicholson - 1809
...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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Elements of Geometry

Adrien Marie Legendre - 1819 - 208 sider
...y would be so, they become therefore imaginary in the case under consideration, when q exceeds ?-. It will be perceived then from what has been said,...greater than the square of half the coefficient of thcJirst power of the unknown quantity, tins equation can have only imaginary roots. 115. The expressions...
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volum 1

William Nicholson - 1819
...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 - 1820 - 332 sider
...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, Volum 7;Volum 13

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1821
...of the question, the necessity of the roots being imaginary in an equation, of which the known term is negative in the second member, and greater than...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 - 224 sider
...y would be so, they become therefore imaginary in the case under consideration, when l{ exceeds—. It will be perceived then from what has been said,...quantity, this equation can have only imaginary roots. 115. The expressions > V'"^, a + \s~-bi and, in general, those, which involve the square root of a...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1827 - 332 sider
...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 ...

1836 - 472 sider
...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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Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ...

Jeremiah Day, James Bates Thomson - 1844 - 252 sider
...first term. 257. From this principle is derived the following METHOD FOR COMPLETING THE SQUARE. 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. 258. It will be observed that there is nothing peculiar in...
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