Elements of Algebra

298 ELEMENTS OF ALGEBRA. SECT. IV. that which we explained first; for it applies successfully to all kinds of equations: whereas the other often requires the equation to be prepared in a certain manner, without which it cannot be employed; and of this we have seen a proof in different examples. QUESTIONS FOR PRACTICE. 1. Given $x^3 + 2x^2 - 23x - 70 = 0$, to find $x$. Ans. $x = 5.13450$. 2. Given $x^3 - 15x^2 + 63x - 50 = 0$, to find $x$. Ans. $x = 1.028039$. 3. Given $x^4 - 3x^2 - 75x = 10000$, to find $x$. Ans. $x = 10.2615$. 4. Given $x^5 + 2x^4 + 3x^3 + 4x^2 + 5x = 54321$, to find $x$. Ans. $x = 8.4144$. 5. Let $120x^3 + 3657x^2 - 38059x = 8007115$, to find $x$. Ans. $x = 34.6532$. END OF PART I.