...trinomial equal to zero and reduce the resulting equation. 131. Add to both members of the equation the square of half the coefficient of the first power of the unknown quantity. Connect each root with its signs changed to the lowest power of the literal quantity. 132. Multiply...

...third term in Answer : Take half of the 12 and square it. Thus : RULE FOR COMPLETING THE SQUARE : Add the square of half the coefficient of the first power of the unknown number. 3. x*— 12ж = 13. Find the values of x. Process: (1) 2* -12 ж =13. Completing the sq., (2)...

...superposition. In the case of a quadratic, the quantity superposed is (I speak of the ordinary process) the square of half the coefficient of the first power of the unknown. This superposition is followed by a Phil. Mag. S. 3. No. 253. Suppl. Vol. 37. 2 K contraction, the...

...theorem, is impossible. If, then, any problem furnishes an equation in which the known term is negative, and greater than the square of half the coefficient of the first power of the unknown quantity, we infer, that the conditions of the problem are incompatible with each other. The following is an...

...in the third and fourth forms, when q is greater than p2, that is, when the known term is negative, and greater than the square of half the coefficient of the first power of x, beth values of the unknown quantity are impossible. What is the cause of this impossibility? To...

...in the third and fourth forms, when q is greater than p*, that is, when the known term is negative, and greater than the square of half the coefficient of the first power of x, both values of the unknown quantity are impossible. What is the cause of this impossibility? To...