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 112by James Wood - 1845 - 287 pagesFull view - About this book
| 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... | |
| 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... | |
| 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 +... | |
| 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... | |
| 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... | |
| 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.... | |
| 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,... | |
| 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,... | |
| 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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