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roots to be 5 and -5. Changing the signs of the alternate terms
of the equation, we obtain the decimal part of the negative root, by
the following

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EXPLANATION.-We proceed as in the preceding example till we
obtain the terms marked (2), in the operation. Dividing 10.2929 by
321.302, we obtain .03 for the next figure of the root.

At this point we commence to apply decimal contractions, accord
ing to the principles employed in the contracted method of cube
root; (243). Let it be observed, that each contracted term in
the operation contains one redundant figure at the right.

Commencing with column IV, we have 21.8X.03.65, which added to column III gives 148.49. Then 148.49X.03 4.455, which added to column II gives 325.757. Then 325.757.03 = 9.7727, which added to column I gives .5202. Again adding .65 to column III, we have 149.14. Then 149.14.03 = 4.474, which added to column II gives 330.23, after dropping one place. Again, adding .65 to column III gives 150 after dropping two places. In like manner we continue till the work is finished.

NOTE.—Observe, as a general rule, to contract the several columns, for each root figure, as follows:-Column I, 0 place; column II, 1 place; column III, 2 places; column IV, 3 places; and so on.

Find the real roots of the following equations:

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NOTE.-Full solutions of the examples above may be found in the Key.

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