...this principle is derived tho following METHOD' FOB COMPLETINO THE SQUARE. Take the square of half Hie co-efficient of the first power of the unknown quantity, and add it to both sides of the equation. It will be observed that there is nothing peculiar in the solution of adjected quadratics, except the...

...unknown quantity, its value is found by transposing the second term. SCH. I. — 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 SQDAKE. There are...

...the roots of %х>— \х + Щ = Щ, and verify. 7, and — 6-J-. Scholium. — 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. There are...

...unknown quantity, its value is found by transposing the second term. 8сн. 1. — 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. There are...

...second member (q) of an equation of the second degree be negative, it cannot be numerically greater than the square of half the coefficient of the first power of the unknown quantity, if the roots be real. p-\-d= the greater quantity, and p—d the less. If q represent their product,...

...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...

...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...

...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...