Question

Solve by completing the square:

`1/2 x^2 - sqrt11 x + 1 = 0`

Answer 1

Given:

`1/2 x^2 - sqrt11 x + 1 = 0`

Multiply the entire equation by 2 to make the coefficient of x² equal to 1:

`x^2 - 2 sqrt11 x + 2 = 0`

` x^2 - 2 sqrt11 x + -2`

Complete the square:

Coefficient of x = `-2sqrt11`

Half = `-sqrt11`

Square = `(sqrt11)^2 = 11`

`x^2 - 2 sqrt11 x + 11 =−2+11=9`

`(x-sqrt11)^2 = 9`

`x - sqrt11 = +- 3`

`x = sqrt11 + 3 or x = sqrt11 - 3`