Question

How do you solve using the completing the square method `x^2 − x = 30`?

Answer 1

`x=-5,6`

Explanation:

`x^2-x=30`

1) Check the constant term is on the right side if not bring it to the right side .
2) Check the coefficient of x^2 is 1 if not Make the coefficient of x^2 as 1

`x^2-x=30`

Add both side `(coefficient of x/2)^2`

Coefficient of x is -1 so add `(-1/2)^2`, both side

`x^2-x+(1/2)^2=30 +(1/2)^2` use the identity `(a-b)^2=a^2-2ab+b^2`

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

`(x-1/2)^2=30+1/4`

`(x-1/2)^2=121/4`
squaring on both side

`(x-1/2)=+-sqrt(121/4)`

`(x-1/2)=+-11/2`

`x=1/2+11/2, x=1/2-11/2`
`x=12/2 or x=-10/2`

`x=-5,6`