Question

Rewrite the equation by completing the square.

x^2-x-20=0
(x+ ? )^2= ?

please help me

Answer 1

Rewrite the equation by completing the square.

x^2 - x - 20 = 0

(x+ ? )^2= ?

Answer 2

`(x-(1)/(2))^2=(81)/(4)`

Explanation:

Hi there!

`x^2-x-20=0`

This equation is written in the form
`ax^2+bx+c=0`. First, use partial factoring:

`(x^2-x)-20=0`

For x^2-x, the b value is -1 in
`ax^2+bx+c`. To complete the square, take the square of half of 1 and add it in the parentheses as the c value:

`(x^2-x+(1)/(2)^2 )-20=0`

However, when adding values to one side of the equation, we must to the same to the other side:

`(x^2-x+(1)/(2)^2 )-20=(1)/(2)^2`

Complete the square:

`(x-(1)/(2))^2-20=(1)/(4)`

Move 20 to the other side

`(x-(1)/(4))^2=(1)/(4)+20\\(x-(1)/(2))^2=(81)/(4)`

I hope this helps!