This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1878 Excerpt: ...the first power enters as well as the square, as x1--3x + 2 = 0, &c. 122. Pure Quadratics are solved, as in simple equation, by collecting the unknown quantities on one side, and the known quantities on the other. We shall thus find the value of x2, and thence the value of x, to which we must prefix the double sign ( + ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1878 Excerpt: ...the first power enters as well as the square, as x1--3x + 2 = 0, &c. 122. Pure Quadratics are solved, as in simple equation, by collecting the unknown quantities on one side, and the known quantities on the other. We shall thus find the value of x2, and thence the value of x, to which we must prefix the double sign ( + ). by this step, the first side becomes a complete square; and taking the square root of each side, prefixing, as before, the double sign to that of the latter, we have x + p = "kjP--q, and.r=--p _ ip2--q; which expression gives us, according as we take the upper or lower sign, two roots of the quadratic. 124. From the preceding we derive the following Rule for the solution of an adfected quadratic: Reduce it to its simplest form; set the terms involving x2 and x on one side (the coeff. of x being +1), and the known quantity on the other; then, if we add the square of half the coeff. of x to each side, the first will become a complete square; and taking the square root of each, prefixing the double sign to the second, we shall obtain, as above, the two roots of the equation. Ex.1. 2-6.r = 7. Here x3-6+9 = 7+9 = 16; whence.r--3 = +4, and x = 3+4 = 7, or x = 3--4=---1; so that 7 and-1 are the two roots of the equation. Ex.2. a-, +14x = 95. Here r2+14.r+49 = 95+49 = 144; whence.r+7 = +12, and.r=-7+12 = 5, or.r=-7-12 =-19. Ex. SS. 1. x--2.r = 8. 2..i-'+10.r=-9. 3. a?-14 = 120. 4.-12 =-35. 6. x2+32.r=320. C. a.-'+100.r=1100. We shall now give a few examples of quadratic equations of two unknowns. The solution of these is generally more difficult: but there are three cases of frequent occurrence, for which the following observations will be useful. 134. (i) Express, when possible, by means of one of the equations, eith...
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