Question

What value of p will make the expression below a perfect square? x^2 - x + P

Answer 1

p =
`(1)/(4)`

Explanation:

To make a perfect square

add ( half the coefficient of the x- term )² to x² - x, that is

x² + 2(-
`(1)/(2)` )x +
`(1)/(4)` with p =
`(1)/(4)` , thus

x² - x = (x -
`(1)/(2)` )² +
`\frac{1}4}`

Answer 2

x^2 - x + 1/4

Explanation:

To complete the square

x^2 - x + P

Take the coefficient of x

-1

Divide by 2

-1/2

Then square it

(-1/2)^2

1/4

Add this to complete the square

x^2 - x + 1/4