...whatever, positive or negative, integral or fractional. Let it be required to solve the equation я? + 3x = 4. In any trinomial square (Art. 108), the middle...square root of the quantity which must be added to я? + 3x to make it a perfect square, is —, or — . 2ж 2 3 9 Adding to both members the square of -,...

...term by twice the square root of the first. 1. Solve the equation 9яr — 5ж= 4. The quotient of the second term divided by twice the square root of the first, is -. Adding the square of - to both members, 9ж2_5ж + 25 = 4 + 25 = !6_9. 36 36 36 Extracting the...

...the product of the square roots of the other two (Art. 41), the square root of the third term must be equal to the second term divided by twice the square root of the first term. Hence, dividing 4abx by twice the square root of 4o2o;2, ie, by 4a», and adding the square of...

...COMPLETING THE SQUARE. 261. Every affected quadratic equation cau be reduced to the form a? +px = q ; where p and q represent any quantities whatever, positive...Therefore the square root of the quantity which must be 3ж 3 added to a? + 3x to make it a perfect square, is — , or — . 2ж 2 » 39 Adding to both members...

...positive, and -the second term plus or minus twice the product of their square roots (Art. 125). Therefore the square root of the third term is equal to the...term divided by twice the square root of the first. Hence the square root of the expression which must be added to 9a? + 2x to make it a perfect square,...

...exactly found. Note 2. — A trinomial is a complete square if, when arranged by one of its letters, the middle term is twice the product of the square roots of the first and last terms; that is, when the square of the middle term is four times the product of the first and...

...-f- 64 can be written as the difference of two squares. Since a trinomial is a perfect square when the middle term is twice the product of the square roots of the first and last terms, it is obvious that we must add a2V to the middle term of a4 + a2¿2 + 64 to make it a perfect...

...a2¿2 + b4 can be written as the difference of two squares. Since a trinomial is a perfect square when the middle term is twice the product of the square roots of the first and last terms, it is obvious that we must add dV to the middle term of a4 + a2¿2 + 54 to make it a perfect...

...4>j' - 100 X2у2 REVIEW IN FACTORING. Page 87. f 61. This is a perfect square, the middle tern> being twice the product of the square roots of the first and third ; therefore, the factors are : [(^ - xy)- (xy - 1)] [(x2 - xy)-(xy - 1)], = (x2-2xу+ 1)(x2-2xу +...

...positive, and the second term plus (or minus) twice the product of their square roots (§ 96). Then, the square root of the third term is equal to the...term divided by twice the square root of the first. Hence, the square root of the expression which must be о ~ о added to я? + 3 x to make it a perfect...