Solve (2x)^2/3.2=3.08*10^-4

$$\frac { ( 2 x ) ^ { 2 } } { 3.2 } = 3.08 \times 10 ^ { - 4 }$$

Solve for x

$$x=\frac{\sqrt{385}}{1250}\approx 0.015697133$$

$$x=-\frac{\sqrt{385}}{1250}\approx -0.015697133$$

Steps by Finding Square Root

Expand \left(2x\right)^{2}.

$$\frac{2^{2}x^{2}}{3.2}=3.08\times 10^{-4}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{2}}{3.2}=3.08\times 10^{-4}$$

Divide 4x^{2} by 3.2 to get 1.25x^{2}.

$$1.25x^{2}=3.08\times 10^{-4}$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$1.25x^{2}=3.08\times \frac{1}{10000}$$

Multiply 3.08 and \frac{1}{10000} to get \frac{77}{250000}.

$$1.25x^{2}=\frac{77}{250000}$$

Divide both sides by 1.25.

$$x^{2}=\frac{\frac{77}{250000}}{1.25}$$

Express \frac{\frac{77}{250000}}{1.25} as a single fraction.

$$x^{2}=\frac{77}{250000\times 1.25}$$

Multiply 250000 and 1.25 to get 312500.

$$x^{2}=\frac{77}{312500}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{385}}{1250} x=-\frac{\sqrt{385}}{1250}$$

Steps Using the Quadratic Formula

Expand \left(2x\right)^{2}.

$$\frac{2^{2}x^{2}}{3.2}=3.08\times 10^{-4}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{2}}{3.2}=3.08\times 10^{-4}$$

Divide 4x^{2} by 3.2 to get 1.25x^{2}.

$$1.25x^{2}=3.08\times 10^{-4}$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$1.25x^{2}=3.08\times \frac{1}{10000}$$

Multiply 3.08 and \frac{1}{10000} to get \frac{77}{250000}.

$$1.25x^{2}=\frac{77}{250000}$$

Subtract \frac{77}{250000} from both sides.

$$1.25x^{2}-\frac{77}{250000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1.25 for a, 0 for b, and -\frac{77}{250000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1.25\left(-\frac{77}{250000}\right)}}{2\times 1.25}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 1.25\left(-\frac{77}{250000}\right)}}{2\times 1.25}$$

Multiply -4 times 1.25.

$$x=\frac{0±\sqrt{-5\left(-\frac{77}{250000}\right)}}{2\times 1.25}$$

Multiply -5 times -\frac{77}{250000}.

$$x=\frac{0±\sqrt{\frac{77}{50000}}}{2\times 1.25}$$

Take the square root of \frac{77}{50000}.

$$x=\frac{0±\frac{\sqrt{385}}{500}}{2\times 1.25}$$

Multiply 2 times 1.25.

$$x=\frac{0±\frac{\sqrt{385}}{500}}{2.5}$$

Now solve the equation x=\frac{0±\frac{\sqrt{385}}{500}}{2.5} when ± is plus.

$$x=\frac{\sqrt{385}}{1250}$$

Now solve the equation x=\frac{0±\frac{\sqrt{385}}{500}}{2.5} when ± is minus.

$$x=-\frac{\sqrt{385}}{1250}$$

The equation is now solved.

$$x=\frac{\sqrt{385}}{1250} x=-\frac{\sqrt{385}}{1250}$$