-12
-7
81. To complete the square of x^2 + 18x, you take half the coefficient of the x term (half of 18 is 9), and square that number (9 squared is 81). To confirm this works, you can now factor x^2 + 18x + 81 and see that it factors as (x+9)(x+9), or (x+9)^2, a perfect square.
49-apex
To complete the square for the expression ( x^2 + 8x ), first take half of the coefficient of ( x ) (which is 8), square it, and add it. Half of 8 is 4, and squaring it gives ( 4^2 = 16 ). Therefore, the number that must be added to ( x^2 + 8x ) to complete the square is 16. Thus, the completed square form is ( (x + 4)^2 ).
To complete the square for the expression (x^2 + 9x), take half of the coefficient of (x) (which is 9), square it, and add that value. Half of 9 is (4.5), and squaring it gives (20.25). Therefore, the number that must be added is (20.25). Thus, the completed square form is ((x + 4.5)^2).
-3
144
-7
49/4 or 12.25
Adding 100 completes the square. { I wonder why you want to complete the square when the expression already factors as x(x-20) }.
81. To complete the square of x^2 + 18x, you take half the coefficient of the x term (half of 18 is 9), and square that number (9 squared is 81). To confirm this works, you can now factor x^2 + 18x + 81 and see that it factors as (x+9)(x+9), or (x+9)^2, a perfect square.
49-apex
To complete the square for the expression ( x^2 + 8x ), first take half of the coefficient of ( x ) (which is 8), square it, and add it. Half of 8 is 4, and squaring it gives ( 4^2 = 16 ). Therefore, the number that must be added to ( x^2 + 8x ) to complete the square is 16. Thus, the completed square form is ( (x + 4)^2 ).
To complete the square for the expression (x^2 + 9x), take half of the coefficient of (x) (which is 9), square it, and add that value. Half of 9 is (4.5), and squaring it gives (20.25). Therefore, the number that must be added is (20.25). Thus, the completed square form is ((x + 4.5)^2).
A polynomial is several terms added together.
9
X^2 + X = 0 halve the linear term (1) and square it then add to both sides X^2 + X + 1/4 = 1/4 factor left; gather terms right (X + 1/2)^2 = 1/4 (X + 1/2)^2 - 1/4 = 0 (-1/2,-1/4) vector and the number 1/4 was added to both sides completing the square