Question

What number must be added to the expression below to complete the square?

x^2 - x

A. 1/2
B. -1/4
C. -1/2
D. 1/4

Answer 1

D. 1/4

Explanation:

a perfect square is written in the form

$(x+a)^2 = x^2 + 2ax +a^2$ (1)

In our problem, we have this perfect square:

$x^2 - x + C$ (2)

with C being unknown. However, by comparing (1) and (2), we know that

$2a=-1$

So, we find

$a=-\frac{1}{2}$

and therefore, the missing term must be

$a^2 = \frac{1}{4}$

so the complete square is

$x^2 -x +\frac{1}{4}$

Answer 2

Answer:

1/4

Step-by-step explanation:

To complete the square, use the formula (b/2)^2

The Quadratic Formula is: a+bx+c

thus a = x^2, b = -1

You then plug in the numbers in the formula above

(b/2)^2 = (-1/2)^2 = (1/2)^2 =1/4