Solve 2/100=5x^2*10^5

$$\frac { 2 } { 100 } = 5 x ^ { 2 } \times 10 ^ { 5 }$$

Solve for x

$$x=\frac{1}{5000}=0.0002$$

$$x=-\frac{1}{5000}=-0.0002$$

Steps Using Difference of Squares

Reduce the fraction \frac{2}{100} to lowest terms by extracting and canceling out 2.

$$\frac{1}{50}=5x^{2}\times 10^{5}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{1}{50}=5x^{2}\times 100000$$

Multiply 5 and 100000 to get 500000.

$$\frac{1}{50}=500000x^{2}$$

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

$$500000x^{2}=\frac{1}{50}$$

Subtract \frac{1}{50} from both sides.

$$500000x^{2}-\frac{1}{50}=0$$

Multiply both sides by 50.

$$25000000x^{2}-1=0$$

Consider 25000000x^{2}-1. Rewrite 25000000x^{2}-1 as \left(5000x\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5000x-1\right)\left(5000x+1\right)=0$$

To find equation solutions, solve 5000x-1=0 and 5000x+1=0.

$$x=\frac{1}{5000} x=-\frac{1}{5000}$$

Steps by Finding Square Root

Reduce the fraction \frac{2}{100} to lowest terms by extracting and canceling out 2.

$$\frac{1}{50}=5x^{2}\times 10^{5}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{1}{50}=5x^{2}\times 100000$$

Multiply 5 and 100000 to get 500000.

$$\frac{1}{50}=500000x^{2}$$

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

$$500000x^{2}=\frac{1}{50}$$

Divide both sides by 500000.

$$x^{2}=\frac{\frac{1}{50}}{500000}$$

Express \frac{\frac{1}{50}}{500000} as a single fraction.

$$x^{2}=\frac{1}{50\times 500000}$$

Multiply 50 and 500000 to get 25000000.

$$x^{2}=\frac{1}{25000000}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{5000} x=-\frac{1}{5000}$$

Steps Using the Quadratic Formula

Reduce the fraction \frac{2}{100} to lowest terms by extracting and canceling out 2.

$$\frac{1}{50}=5x^{2}\times 10^{5}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{1}{50}=5x^{2}\times 100000$$

Multiply 5 and 100000 to get 500000.

$$\frac{1}{50}=500000x^{2}$$

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

$$500000x^{2}=\frac{1}{50}$$

Subtract \frac{1}{50} from both sides.

$$500000x^{2}-\frac{1}{50}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 500000 for a, 0 for b, and -\frac{1}{50} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 500000\left(-\frac{1}{50}\right)}}{2\times 500000}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 500000\left(-\frac{1}{50}\right)}}{2\times 500000}$$

Multiply -4 times 500000.

$$x=\frac{0±\sqrt{-2000000\left(-\frac{1}{50}\right)}}{2\times 500000}$$

Multiply -2000000 times -\frac{1}{50}.

$$x=\frac{0±\sqrt{40000}}{2\times 500000}$$

Take the square root of 40000.

$$x=\frac{0±200}{2\times 500000}$$

Multiply 2 times 500000.

$$x=\frac{0±200}{1000000}$$

Now solve the equation x=\frac{0±200}{1000000} when ± is plus. Reduce the fraction \frac{200}{1000000} to lowest terms by extracting and canceling out 200.

$$x=\frac{1}{5000}$$

Now solve the equation x=\frac{0±200}{1000000} when ± is minus. Reduce the fraction \frac{-200}{1000000} to lowest terms by extracting and canceling out 200.

$$x=-\frac{1}{5000}$$

The equation is now solved.

$$x=\frac{1}{5000} x=-\frac{1}{5000}$$