Solve 3z^2=1024

$$3 z ^ { 2 } = 1024$$

Solve for z

$$z = \frac{32 \sqrt{3}}{3} \approx 18.475208614$$

$$z = -\frac{32 \sqrt{3}}{3} \approx -18.475208614$$

Steps by Finding Square Root

Divide both sides by 3.

$$z^{2}=\frac{1024}{3}$$

Take the square root of both sides of the equation.

$$z=\frac{32\sqrt{3}}{3} z=-\frac{32\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

Divide both sides by 3.

$$z^{2}=\frac{1024}{3}$$

Subtract \frac{1024}{3} from both sides.

$$z^{2}-\frac{1024}{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1024}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-\frac{1024}{3}\right)}}{2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-\frac{1024}{3}\right)}}{2}$$

Multiply -4 times -\frac{1024}{3}.

$$z=\frac{0±\sqrt{\frac{4096}{3}}}{2}$$

Take the square root of \frac{4096}{3}.

$$z=\frac{0±\frac{64\sqrt{3}}{3}}{2}$$

Now solve the equation z=\frac{0±\frac{64\sqrt{3}}{3}}{2} when ± is plus.

$$z=\frac{32\sqrt{3}}{3}$$

Now solve the equation z=\frac{0±\frac{64\sqrt{3}}{3}}{2} when ± is minus.

$$z=-\frac{32\sqrt{3}}{3}$$

The equation is now solved.

$$z=\frac{32\sqrt{3}}{3} z=-\frac{32\sqrt{3}}{3}$$