Solve 21*10^-3=9*10^9*x^2/15*10^-3

$$21 \times { 10 }^{ -3 } = \frac{ 9 \times { 10 }^{ 9 } \times { x }^{ 2 } }{ 15 \times { 10 }^{ -3 } }$$

Solve for x

$$x=\frac{\sqrt{14}}{20000000}\approx 0.000000187$$

$$x=-\frac{\sqrt{14}}{20000000}\approx -0.000000187$$

Steps by Finding Square Root

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$21\times \frac{1}{1000}=\frac{9\times 10^{9}x^{2}}{15\times 10^{-3}}$$

Multiply 21 and \frac{1}{1000} to get \frac{21}{1000}.

$$\frac{21}{1000}=\frac{9\times 10^{9}x^{2}}{15\times 10^{-3}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{21}{1000}=\frac{3\times 10^{9}x^{2}}{5\times 10^{-3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{21}{1000}=\frac{3\times 10^{12}x^{2}}{5}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$\frac{21}{1000}=\frac{3\times 1000000000000x^{2}}{5}$$

Multiply 3 and 1000000000000 to get 3000000000000.

$$\frac{21}{1000}=\frac{3000000000000x^{2}}{5}$$

Divide 3000000000000x^{2} by 5 to get 600000000000x^{2}.

$$\frac{21}{1000}=600000000000x^{2}$$

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

$$600000000000x^{2}=\frac{21}{1000}$$

Divide both sides by 600000000000.

$$x^{2}=\frac{\frac{21}{1000}}{600000000000}$$

Express \frac{\frac{21}{1000}}{600000000000} as a single fraction.

$$x^{2}=\frac{21}{1000\times 600000000000}$$

Multiply 1000 and 600000000000 to get 600000000000000.

$$x^{2}=\frac{21}{600000000000000}$$

Reduce the fraction \frac{21}{600000000000000} to lowest terms by extracting and canceling out 3.

$$x^{2}=\frac{7}{200000000000000}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{14}}{20000000} x=-\frac{\sqrt{14}}{20000000}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$21\times \frac{1}{1000}=\frac{9\times 10^{9}x^{2}}{15\times 10^{-3}}$$

Multiply 21 and \frac{1}{1000} to get \frac{21}{1000}.

$$\frac{21}{1000}=\frac{9\times 10^{9}x^{2}}{15\times 10^{-3}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{21}{1000}=\frac{3\times 10^{9}x^{2}}{5\times 10^{-3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{21}{1000}=\frac{3\times 10^{12}x^{2}}{5}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$\frac{21}{1000}=\frac{3\times 1000000000000x^{2}}{5}$$

Multiply 3 and 1000000000000 to get 3000000000000.

$$\frac{21}{1000}=\frac{3000000000000x^{2}}{5}$$

Divide 3000000000000x^{2} by 5 to get 600000000000x^{2}.

$$\frac{21}{1000}=600000000000x^{2}$$

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

$$600000000000x^{2}=\frac{21}{1000}$$

Subtract \frac{21}{1000} from both sides.

$$600000000000x^{2}-\frac{21}{1000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 600000000000 for a, 0 for b, and -\frac{21}{1000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 600000000000\left(-\frac{21}{1000}\right)}}{2\times 600000000000}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 600000000000\left(-\frac{21}{1000}\right)}}{2\times 600000000000}$$

Multiply -4 times 600000000000.

$$x=\frac{0±\sqrt{-2400000000000\left(-\frac{21}{1000}\right)}}{2\times 600000000000}$$

Multiply -2400000000000 times -\frac{21}{1000}.

$$x=\frac{0±\sqrt{50400000000}}{2\times 600000000000}$$

Take the square root of 50400000000.

$$x=\frac{0±60000\sqrt{14}}{2\times 600000000000}$$

Multiply 2 times 600000000000.

$$x=\frac{0±60000\sqrt{14}}{1200000000000}$$

Now solve the equation x=\frac{0±60000\sqrt{14}}{1200000000000} when ± is plus.

$$x=\frac{\sqrt{14}}{20000000}$$

Now solve the equation x=\frac{0±60000\sqrt{14}}{1200000000000} when ± is minus.

$$x=-\frac{\sqrt{14}}{20000000}$$

The equation is now solved.

$$x=\frac{\sqrt{14}}{20000000} x=-\frac{\sqrt{14}}{20000000}$$