Solve the equation by completing the square.
-$$3 z ^ { 2 } = \frac { 3 } { 2 } z + 2$$
A) $$\frac { - 3 \pm \sqrt { 105 } } { 12 }$$
B) $$\frac { 3 \pm \sqrt { 105 } } { 12 }$$
C) $$\frac { 3 \pm \sqrt { 105 } } { 6 }$$
D) $$\frac { - 3 \pm \sqrt { 57 } } { 6 }$$

Question

Quizplus · Accepted Answer

To solve by completing the square, first rearrange the equation to $3z^2 - \frac{3}{2}z - 2 = 0$. Divide by 3: $z^2 - \frac{1}{2}z = \frac{2}{3}$. Complete the square: $(z - \frac{1}{4})^2 = \frac{2}{3} + \frac{1}{16}$. Solve for $z$ to get the solutions $\frac{3 \pm \sqrt{105}}{12}$.

Solve the Equation by Completing the Square 3z2=32z+23 z ^ { 2 } = \frac { 3 } { 2 } z + 23z2=23​z+2

Solve the Equation by Completing the Square $3 z ^ { 2 } = \frac { 3 } { 2 } z + 2$