Question

Solve by completing the square:

z² − 3z + 1 = 0

Answer 1

Given:

z² − 3z + 1 = 0

Move the constant to the right-hand side

z² − 3z = −1

Take half of the coefficient of z, square it, and add to both sides:

Coefficient of z = −3

Half = `-3/2`

Square = `(3/2)^2 = 9/4`

`z^2 - 3z + 9/4 = -1 + 9/4`

`=> (z -3/2)^2 =5/4`

`z -3/2 = +- sqrt(5/4) = +- sqrt5/2`

Solve for z

`z = 3/2 +- sqrt5/2`

`=> z=(3+-sqrt5)/5`