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

Answer:

Step-by-step explanation:

$\sqrt{2z}$ + 3 = -z

$\sqrt{2z}$ = -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 + $\sqrt{5}$i , -2 - $\sqrt{5}$i

Answer 2

Answer:

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)