...b)2 = «V ± 2 abx + ¿2, it is evident that the expression аV±2аto lacks only the third term, b2, of being a complete square. It will be seen that this...dividing the second term by twice the square root of the Jirst term. 226. Every affected quadratic may be made to assume the form of aV±2eur = c. The first...

...±6)3 = aV ± 2abx + V, it is evident that the expression aV± 2abx lacks only the third term, 62, of being a complete square. 'It will be seen that...third term is the square of the quotient obtained from dividiny the second term by twice the square root of the first term. 282. Every affected quadratic...

...± by — aV ± 2abx -f V, it is evident that the expression aV± 2abx lacks only the third term, V, of being a complete square. It will be seen that this third term is the sguare of the quotient obtained from dividing the second term by twice the square root of the first...

...quadratic equation the coefficient of ж2 is a square number, we may readily complete the square by dividing the second term by twice the square root of the first term, and adding the square of the quotient thus obtained to both members of the equation. That this process...

...coefficient of x2 is 4, 9, 16, or any other perfect square, we may complete the square by adding to each side the square of the quotient obtained from dividing...second term by twice the square root of the first term. Solve 4 x2 - 23 x = - 30. 23 The square root of 4x2 is 2 x, and 23 x divided by twice 2x is — •...

...we may complete the square by adding to each side the square of the quotient obtained from dividiny the second term by twice the square root of the first term. Solve 4ж2 -23 ж = -30. 23 The square root of 4x2 is 2x, and 23 х divided by twice 2x is — 23 Add...

...агх? + 2 abx + b!, it is evident that the third term, W, is the square of the quotient obtained by dividing the second term by twice the square root of the first«, EXAMPLES 1. Solve the equation 5 ж2 + 12 x = 9. SOLUTION 5 *2 + 12 x = 9. Multiplying by 6, 25 x2...

...+ У, its first term is a perfect square. Hence, we multiply the equation by a. iAt2 + abx = ac Its third term is the square of the quotient obtained...second term by twice the square root of the first. JO Hence, we add to each member (abx -т- 2 Va2ж2)2, or — . Hence, the principle, QED PROPOSITION...

...binomial ax ± b, as follows: add to each side of the equation the square of the quotient obtained by dividing the second term by twice the square root of the first term. 3. Extract the square root of each side of the resulting equation. Solve 3X1* — 4x ~ 32. To make...

...azz* + 2 abz + Ъг, it is evident that the third term, №, is the square of the quotient obtained by dividing the second term by twice the square root of the first. EXAMPLES 1. Solve the equation 5 л? + 12 x = 9. SOLUTION 5z2 + 12 z = 9. Multiplying by 6, 25 za +...