Solve z=70000/z

$$z = 70000 / z$$

Solve for z

$$z=100\sqrt{7}\approx 264.575131106$$

$$z=-100\sqrt{7}\approx -264.575131106$$

Steps by Finding Square Root

Subtract \frac{70000}{z} from both sides.

$$z-\frac{70000}{z}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply z times \frac{z}{z}.

$$\frac{zz}{z}-\frac{70000}{z}=0$$

Since \frac{zz}{z} and \frac{70000}{z} have the same denominator, subtract them by subtracting their numerators.

$$\frac{zz-70000}{z}=0$$

Do the multiplications in zz-70000.

$$\frac{z^{2}-70000}{z}=0$$

Variable z cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by z.

$$z^{2}-70000=0$$

Add 70000 to both sides. Anything plus zero gives itself.

$$z^{2}=70000$$

Take the square root of both sides of the equation.

$$z=100\sqrt{7} z=-100\sqrt{7}$$

Steps Using the Quadratic Formula

Subtract \frac{70000}{z} from both sides.

$$z-\frac{70000}{z}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply z times \frac{z}{z}.

$$\frac{zz}{z}-\frac{70000}{z}=0$$

Since \frac{zz}{z} and \frac{70000}{z} have the same denominator, subtract them by subtracting their numerators.

$$\frac{zz-70000}{z}=0$$

Do the multiplications in zz-70000.

$$\frac{z^{2}-70000}{z}=0$$

Variable z cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by z.

$$z^{2}-70000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -70000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-70000\right)}}{2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-70000\right)}}{2}$$

Multiply -4 times -70000.

$$z=\frac{0±\sqrt{280000}}{2}$$

Take the square root of 280000.

$$z=\frac{0±200\sqrt{7}}{2}$$

Now solve the equation z=\frac{0±200\sqrt{7}}{2} when ± is plus.

$$z=100\sqrt{7}$$

Now solve the equation z=\frac{0±200\sqrt{7}}{2} when ± is minus.

$$z=-100\sqrt{7}$$

The equation is now solved.

$$z=100\sqrt{7} z=-100\sqrt{7}$$