Solve 1/10^6+1/x^2=1/25*10^4

$$\frac{ 1 }{ { 10 }^{ 6 } } + \frac{ 1 }{ { x }^{ 2 } } = \frac{ 1 }{ 25 \times { 10 }^{ 4 } }$$

Solve for x

$$x = \frac{1000 \sqrt{3}}{3} \approx 577.35026919$$

$$x = -\frac{1000 \sqrt{3}}{3} \approx -577.35026919$$

Steps by Finding Square Root

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

$$\frac{1}{1000000}x^{2}+1=\frac{1}{250000}x^{2}$$

Subtract \frac{1}{250000}x^{2} from both sides.

$$\frac{1}{1000000}x^{2}+1-\frac{1}{250000}x^{2}=0$$

Combine \frac{1}{1000000}x^{2} and -\frac{1}{250000}x^{2} to get -\frac{3}{1000000}x^{2}.

$$-\frac{3}{1000000}x^{2}+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{3}{1000000}x^{2}=-1$$

Multiply both sides by -\frac{1000000}{3}, the reciprocal of -\frac{3}{1000000}.

$$x^{2}=-\left(-\frac{1000000}{3}\right)$$

Multiply -1 and -\frac{1000000}{3} to get \frac{1000000}{3}.

$$x^{2}=\frac{1000000}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{1000\sqrt{3}}{3} x=-\frac{1000\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

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

$$\frac{1}{1000000}x^{2}+1=\frac{1}{250000}x^{2}$$

Subtract \frac{1}{250000}x^{2} from both sides.

$$\frac{1}{1000000}x^{2}+1-\frac{1}{250000}x^{2}=0$$

Combine \frac{1}{1000000}x^{2} and -\frac{1}{250000}x^{2} to get -\frac{3}{1000000}x^{2}.

$$-\frac{3}{1000000}x^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{3}{1000000} for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{3}{1000000}\right)}}{2\left(-\frac{3}{1000000}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{3}{1000000}\right)}}{2\left(-\frac{3}{1000000}\right)}$$

Multiply -4 times -\frac{3}{1000000}.

$$x=\frac{0±\sqrt{\frac{3}{250000}}}{2\left(-\frac{3}{1000000}\right)}$$

Take the square root of \frac{3}{250000}.

$$x=\frac{0±\frac{\sqrt{3}}{500}}{2\left(-\frac{3}{1000000}\right)}$$

Multiply 2 times -\frac{3}{1000000}.

$$x=\frac{0±\frac{\sqrt{3}}{500}}{-\frac{3}{500000}}$$

Now solve the equation x=\frac{0±\frac{\sqrt{3}}{500}}{-\frac{3}{500000}} when ± is plus.

$$x=-\frac{1000\sqrt{3}}{3}$$

Now solve the equation x=\frac{0±\frac{\sqrt{3}}{500}}{-\frac{3}{500000}} when ± is minus.

$$x=\frac{1000\sqrt{3}}{3}$$

The equation is now solved.

$$x=-\frac{1000\sqrt{3}}{3} x=\frac{1000\sqrt{3}}{3}$$