Question

Question #35aac

Answer 1

Assuming you meant to find solutions for `1/2x^2-4x+4=0`,

`x= +-2sqrt(2) +4`

Explanation:

Firstly, take out the `1/2` term and complete the square as usual

`1/2x^2-4x+4 = 0`
`1/2[x^2-8x+8] = 0`
`1/2[(x-4)^2 -8] = 0`
`1/2(x-4)^2 -4 = 0`

Now solve for `x`,

`1/2(x-4)^2= 4`
`(x-4)^2 = 8`
`x-4= +-sqrt(8)`
`x= +-sqrt(8)+4`

And simplify the root term

`x= +-(sqrt(4) * sqrt(2)) +4`
`x= +-2sqrt(2) +4`