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
Complete the square. X^2 + 2X halve the linear term ( 2 ), square it and add to polynomial X^2 + 2X + 1
121
25
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.
64
Complete the square. X^2 + 2X halve the linear term ( 2 ), square it and add to polynomial X^2 + 2X + 1
121
None, it involves the square root of a negative number so the roots are imaginary.
No. by definition, the polynomial should contain an integer as exponent and square root 1/2 is not an integer.
25
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.
64
324
15j2(j + 2)
49
49
49-apex