Solve 4x^2=1.066*10^-4

$$4 x ^ { 2 } = 1.066 \times 10 ^ { - 4 }$$

Solve for x

$$x=\frac{\sqrt{2665}}{10000}\approx 0.005162364$$

$$x=-\frac{\sqrt{2665}}{10000}\approx -0.005162364$$

Steps by Finding Square Root

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

$$4x^{2}=1.066\times \frac{1}{10000}$$

Multiply 1.066 and \frac{1}{10000} to get \frac{533}{5000000}.

$$4x^{2}=\frac{533}{5000000}$$

Divide both sides by 4.

$$x^{2}=\frac{\frac{533}{5000000}}{4}$$

Express \frac{\frac{533}{5000000}}{4} as a single fraction.

$$x^{2}=\frac{533}{5000000\times 4}$$

Multiply 5000000 and 4 to get 20000000.

$$x^{2}=\frac{533}{20000000}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{2665}}{10000} x=-\frac{\sqrt{2665}}{10000}$$

Steps Using the Quadratic Formula

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

$$4x^{2}=1.066\times \frac{1}{10000}$$

Multiply 1.066 and \frac{1}{10000} to get \frac{533}{5000000}.

$$4x^{2}=\frac{533}{5000000}$$

Subtract \frac{533}{5000000} from both sides.

$$4x^{2}-\frac{533}{5000000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -\frac{533}{5000000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-\frac{533}{5000000}\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-\frac{533}{5000000}\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-\frac{533}{5000000}\right)}}{2\times 4}$$

Multiply -16 times -\frac{533}{5000000}.

$$x=\frac{0±\sqrt{\frac{533}{312500}}}{2\times 4}$$

Take the square root of \frac{533}{312500}.

$$x=\frac{0±\frac{\sqrt{2665}}{1250}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±\frac{\sqrt{2665}}{1250}}{8}$$

Now solve the equation x=\frac{0±\frac{\sqrt{2665}}{1250}}{8} when ± is plus.

$$x=\frac{\sqrt{2665}}{10000}$$

Now solve the equation x=\frac{0±\frac{\sqrt{2665}}{1250}}{8} when ± is minus.

$$x=-\frac{\sqrt{2665}}{10000}$$

The equation is now solved.

$$x=\frac{\sqrt{2665}}{10000} x=-\frac{\sqrt{2665}}{10000}$$