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" This process of adding the square of half the coefficient of the first power of the unknown quantity to the first member, in order to make it a perfect square, is called COMPLETING THE SQUARE. "
The elements of algebra - Page 112
by James Wood - 1845 - 287 pages
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The popular educator, Volumes 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 ..., Volume 1

William Nicholson - Natural history - 1809
...negative, change the signs of 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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The Eclectic review. vol. 1-New [8th]

1810
...Rule. Reduce the proposed equation to one of the two following forms. 1. • xl + ax = b 2. y_ay = i ' Add to both sides the square of half the coefficient of the unknown quantity in the second term, in order to make the first side a perfect square, as 2. y-ay +...
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volume 1

William Nicholson - Natural history - 1819
...negative, change the signs of 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...the unknown quantity, by which means the first side 6f the equation is made a complete square, and the other consists of known quantities ; and by extracting...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1820 - 332 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 7; Volume 13

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - North American review and miscellaneous journal - 1821
...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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The young man's best companion, and book of general knowledge

L. Murray - 1821
...of the equation by it, so that the coefficient of the square •of the unknown quantity may be 1. 3. Add to both sides the square of half the coefficient of the unknown quantity, and the side of the equation involving the unknown quantity will be a complete square....
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Elements of Algebra

Silvestre François Lacroix - Algebra - 1825 - 276 pages
...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 v/"^6, a + <S~—i>, and, in general,...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 pages
...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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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1827 - 332 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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