...210=205— 3z»+5. Transposing and reducing, ar»+12T=420. Dividing by the coefficient of T J , Completing the square by adding to each side the square of half the coefficient of the second term, r a +4T+4=140-|-4, or Extracting the root, x+2= ± VH4 = ±12 .-. x=— 2±12. Hence...

...may be solved in the usual manner. EXAMPLE 1. Reduce the equation x2 — lOa; = — 16. Completing the square by adding to each side the square of half the coefficient of the second term, 3? — IQx + 25 = 25 — 16 = 9. Extracting the root x — 5 = +.3. Hence, 2=5^3 =...

...may be solved in the usual manner. EXAMPLE 1. Reduce the equation ж2 — ICte = — 16. Completing the square by adding to each side the square of half the coefficient of the second term, x2 — Wx + 25 = 25 — 16 = 9. Extracting the root x — 5 = +.3. Hence, ж=5;+3...

...magnitude we are seeking to make up the square. To solve an adfected quadratic equation, as x2 +4x= 12, we complete the square by adding to each side the square of half the co-efficient 4 ; then z2 +4z+4= 12 + 4= 16 ; extracting the square root, z + 2=4 .-.x =2. PROP. 6. — THEOR. If...

...and reducing, 3 t* + 12 x = 430 Dividing by the coefficient of x *, я * -j- 4 л1 = 1-Ю Completing the square by adding to each side the square of half the ооетсмш! «f the second term, z* + 4* + 4 = HO + 4 Or, (z + 2) « = l M Extracting the root,...

...°r -~4SUMMABT. (1.) If the quadratic equation be not a perfect square, it may generally be made one by adding to each side the square of half the coefficient of the term containing the simple power of x. (2.) If there be no numerical coefficient to the second...

...necessary, we now change all the signs, so that the coefficient of a;" may be + 1. Then completing the square by adding to each side the square of half the coefficient of x, we have a \2a/ 4a a extracting the square root, therefore, 2o 2a Thus, if we represent the two roots...

...arrange it until all the terms involving x are on the first side, and the coefficient ofyfis unity. 2. COMPLETE THE SQUARE by adding to each side the SQUARE OF HALF the coefficient ofx. 3. Take the square root of each side, put a double sign to the second side, and transpose the...

...transposition. Multiply each side by 4, and (4г)' -43(4x)= — 280. Complete the square on the left side by adding to each side the square of half the coefficient of the first power of the unknown quantity, .-. (4.,)- 43(4.,) + = -280=125, 44 4 extracting the square...

...may be obtained as follows : — • f(x) may be written ax'2 + bx + c = Q. Then x* + -x— — . aa Adding to each side the square of half the coefficient of x, or &\2 i. «- 1 , we have xv •'• *— 85*— S— .................... (1) The following important...