Question

Solve: √2z+3 = - z. If there are multiple solutions, list them separated by a comma, e.g., 1, 2. If there is no solution,

enter Ø.

Answer 1

If you mean √2z + 3 = -z, the answer is ∅

If you mean √2 z + 3 = -z

√2 z + 3 = -z

√2 z = -z - 3

√2 z + z = - 3

z(√2 + 1) = -3

z = -3 / (√2 + 1)

z = -3 (√2 - 1)

Answer 2

Explanation:

`√(2z)` + 3 = -z

`√(2z)` = -z - 3

Square both sides , we have

2z =
`(-z-3)^(2)`

2z =
`z^(2)` + 6z + 9

re arranging the equation , we have

`z^(2)` + 6z - 2z + 9 = 0

`z^(2)` + 4z + 9 = 0

This will give a complex roots , solving by quadratic formula

z = -2 +
`√(5)`i , -2 -
`√(5)`i