Solve 50000=(1000/x)^2*5

$$50000 = ( \frac { 1000 } { x } ) ^ { 2 } \times 5$$

Solve for x

$$x=10$$

$$x=-10$$

Steps by Finding Square Root

Divide both sides by 5.

$$\frac{50000}{5}=\left(\frac{1000}{x}\right)^{2}$$

Divide 50000 by 5 to get 10000.

$$10000=\left(\frac{1000}{x}\right)^{2}$$

To raise \frac{1000}{x} to a power, raise both numerator and denominator to the power and then divide.

$$10000=\frac{1000^{2}}{x^{2}}$$

Calculate 1000 to the power of 2 and get 1000000.

$$10000=\frac{1000000}{x^{2}}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1000000}{x^{2}}=10000$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$1000000=10000x^{2}$$

Divide both sides by 10000.

$$\frac{1000000}{10000}=x^{2}$$

Divide 1000000 by 10000 to get 100.

$$100=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=100$$

Take the square root of both sides of the equation.

$$x=10 x=-10$$

Steps Using the Quadratic Formula

Divide both sides by 5.

$$\frac{50000}{5}=\left(\frac{1000}{x}\right)^{2}$$

Divide 50000 by 5 to get 10000.

$$10000=\left(\frac{1000}{x}\right)^{2}$$

To raise \frac{1000}{x} to a power, raise both numerator and denominator to the power and then divide.

$$10000=\frac{1000^{2}}{x^{2}}$$

Calculate 1000 to the power of 2 and get 1000000.

$$10000=\frac{1000000}{x^{2}}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1000000}{x^{2}}=10000$$

Subtract 10000 from both sides.

$$\frac{1000000}{x^{2}}-10000=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 10000 times \frac{x^{2}}{x^{2}}.

$$\frac{1000000}{x^{2}}-\frac{10000x^{2}}{x^{2}}=0$$

Since \frac{1000000}{x^{2}} and \frac{10000x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1000000-10000x^{2}}{x^{2}}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.

$$1000000-10000x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-10000x^{2}+1000000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -10000 for a, 0 for b, and 1000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-10000\right)\times 1000000}}{2\left(-10000\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-10000\right)\times 1000000}}{2\left(-10000\right)}$$

Multiply -4 times -10000.

$$x=\frac{0±\sqrt{40000\times 1000000}}{2\left(-10000\right)}$$

Multiply 40000 times 1000000.

$$x=\frac{0±\sqrt{40000000000}}{2\left(-10000\right)}$$

Take the square root of 40000000000.

$$x=\frac{0±200000}{2\left(-10000\right)}$$

Multiply 2 times -10000.

$$x=\frac{0±200000}{-20000}$$

Now solve the equation x=\frac{0±200000}{-20000} when ± is plus. Divide 200000 by -20000.

$$x=-10$$

Now solve the equation x=\frac{0±200000}{-20000} when ± is minus. Divide -200000 by -20000.

$$x=10$$

The equation is now solved.

$$x=-10 x=10$$