Solve q^2=2.16*10^-19

$$q ^ { 2 } = 2.16 \times 10 ^ { - 19 }$$

Solve for q

$$q=\frac{3\sqrt{15}}{25000000000}\approx 4.647580015 \cdot 10^{-10}$$

$$q=-\frac{3\sqrt{15}}{25000000000}\approx -4.647580015 \cdot 10^{-10}$$

Steps by Finding Square Root

Calculate 10 to the power of -19 and get \frac{1}{10000000000000000000}.

$$q^{2}=2.16\times \frac{1}{10000000000000000000}$$

Multiply 2.16 and \frac{1}{10000000000000000000} to get \frac{27}{125000000000000000000}.

$$q^{2}=\frac{27}{125000000000000000000}$$

Take the square root of both sides of the equation.

$$q=\frac{3\sqrt{15}}{25000000000} q=-\frac{3\sqrt{15}}{25000000000}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of -19 and get \frac{1}{10000000000000000000}.

$$q^{2}=2.16\times \frac{1}{10000000000000000000}$$

Multiply 2.16 and \frac{1}{10000000000000000000} to get \frac{27}{125000000000000000000}.

$$q^{2}=\frac{27}{125000000000000000000}$$

Subtract \frac{27}{125000000000000000000} from both sides.

$$q^{2}-\frac{27}{125000000000000000000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{27}{125000000000000000000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{0±\sqrt{0^{2}-4\left(-\frac{27}{125000000000000000000}\right)}}{2}$$

Square 0.

$$q=\frac{0±\sqrt{-4\left(-\frac{27}{125000000000000000000}\right)}}{2}$$

Multiply -4 times -\frac{27}{125000000000000000000}.

$$q=\frac{0±\sqrt{\frac{27}{31250000000000000000}}}{2}$$

Take the square root of \frac{27}{31250000000000000000}.

$$q=\frac{0±\frac{3\sqrt{15}}{12500000000}}{2}$$

Now solve the equation q=\frac{0±\frac{3\sqrt{15}}{12500000000}}{2} when ± is plus.

$$q=\frac{3\sqrt{15}}{25000000000}$$

Now solve the equation q=\frac{0±\frac{3\sqrt{15}}{12500000000}}{2} when ± is minus.

$$q=-\frac{3\sqrt{15}}{25000000000}$$

The equation is now solved.

$$q=\frac{3\sqrt{15}}{25000000000} q=-\frac{3\sqrt{15}}{25000000000}$$