Solve 0.02=0.5*0.0005*x^2

$$0.02=0.5 \times 0.0005 \times { x }^{ 2 }$$

Solve for x

$$x=4\sqrt{5}\approx 8.94427191$$

$$x=-4\sqrt{5}\approx -8.94427191$$

Steps by Finding Square Root

Multiply 0.5 and 0.0005 to get 0.00025.

$$0.02=0.00025x^{2}$$

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

$$0.00025x^{2}=0.02$$

Divide both sides by 0.00025.

$$x^{2}=\frac{0.02}{0.00025}$$

Expand \frac{0.02}{0.00025} by multiplying both numerator and the denominator by 100000.

$$x^{2}=\frac{2000}{25}$$

Divide 2000 by 25 to get 80.

$$x^{2}=80$$

Take the square root of both sides of the equation.

$$x=4\sqrt{5} x=-4\sqrt{5}$$

Steps Using the Quadratic Formula

Multiply 0.5 and 0.0005 to get 0.00025.

$$0.02=0.00025x^{2}$$

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

$$0.00025x^{2}=0.02$$

Subtract 0.02 from both sides.

$$0.00025x^{2}-0.02=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.00025 for a, 0 for b, and -0.02 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 0.00025\left(-0.02\right)}}{2\times 0.00025}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 0.00025\left(-0.02\right)}}{2\times 0.00025}$$

Multiply -4 times 0.00025.

$$x=\frac{0±\sqrt{-0.001\left(-0.02\right)}}{2\times 0.00025}$$

Multiply -0.001 times -0.02 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{0.00002}}{2\times 0.00025}$$

Take the square root of 0.00002.

$$x=\frac{0±\frac{\sqrt{5}}{500}}{2\times 0.00025}$$

Multiply 2 times 0.00025.

$$x=\frac{0±\frac{\sqrt{5}}{500}}{0.0005}$$

Now solve the equation x=\frac{0±\frac{\sqrt{5}}{500}}{0.0005} when ± is plus.

$$x=4\sqrt{5}$$

Now solve the equation x=\frac{0±\frac{\sqrt{5}}{500}}{0.0005} when ± is minus.

$$x=-4\sqrt{5}$$

The equation is now solved.

$$x=4\sqrt{5} x=-4\sqrt{5}$$