Solve 21*10^-3=9*10^9*x^2/{left(15*10^-3right)^2}

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

Solve for x

$$x=\frac{\sqrt{21}}{200000000}\approx 0.000000023$$

$$x=-\frac{\sqrt{21}}{200000000}\approx -0.000000023$$

Steps by Finding Square Root

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

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

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

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

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{21}{1000}=\frac{9\times 1000000000x^{2}}{\left(15\times 10^{-3}\right)^{2}}$$

Multiply 9 and 1000000000 to get 9000000000.

$$\frac{21}{1000}=\frac{9000000000x^{2}}{\left(15\times 10^{-3}\right)^{2}}$$

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

$$\frac{21}{1000}=\frac{9000000000x^{2}}{\left(15\times \frac{1}{1000}\right)^{2}}$$

Multiply 15 and \frac{1}{1000} to get \frac{3}{200}.

$$\frac{21}{1000}=\frac{9000000000x^{2}}{\left(\frac{3}{200}\right)^{2}}$$

Calculate \frac{3}{200} to the power of 2 and get \frac{9}{40000}.

$$\frac{21}{1000}=\frac{9000000000x^{2}}{\frac{9}{40000}}$$

Divide 9000000000x^{2} by \frac{9}{40000} to get 40000000000000x^{2}.

$$\frac{21}{1000}=40000000000000x^{2}$$

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

$$40000000000000x^{2}=\frac{21}{1000}$$

Divide both sides by 40000000000000.

$$x^{2}=\frac{\frac{21}{1000}}{40000000000000}$$

Express \frac{\frac{21}{1000}}{40000000000000} as a single fraction.

$$x^{2}=\frac{21}{1000\times 40000000000000}$$

Multiply 1000 and 40000000000000 to get 40000000000000000.

$$x^{2}=\frac{21}{40000000000000000}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{21}}{200000000} x=-\frac{\sqrt{21}}{200000000}$$

Steps Using the Quadratic Formula

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

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

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

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

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{21}{1000}=\frac{9\times 1000000000x^{2}}{\left(15\times 10^{-3}\right)^{2}}$$

Multiply 9 and 1000000000 to get 9000000000.

$$\frac{21}{1000}=\frac{9000000000x^{2}}{\left(15\times 10^{-3}\right)^{2}}$$

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

$$\frac{21}{1000}=\frac{9000000000x^{2}}{\left(15\times \frac{1}{1000}\right)^{2}}$$

Multiply 15 and \frac{1}{1000} to get \frac{3}{200}.

$$\frac{21}{1000}=\frac{9000000000x^{2}}{\left(\frac{3}{200}\right)^{2}}$$

Calculate \frac{3}{200} to the power of 2 and get \frac{9}{40000}.

$$\frac{21}{1000}=\frac{9000000000x^{2}}{\frac{9}{40000}}$$

Divide 9000000000x^{2} by \frac{9}{40000} to get 40000000000000x^{2}.

$$\frac{21}{1000}=40000000000000x^{2}$$

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

$$40000000000000x^{2}=\frac{21}{1000}$$

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

$$40000000000000x^{2}-\frac{21}{1000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 40000000000000 for a, 0 for b, and -\frac{21}{1000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 40000000000000\left(-\frac{21}{1000}\right)}}{2\times 40000000000000}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 40000000000000\left(-\frac{21}{1000}\right)}}{2\times 40000000000000}$$

Multiply -4 times 40000000000000.

$$x=\frac{0±\sqrt{-160000000000000\left(-\frac{21}{1000}\right)}}{2\times 40000000000000}$$

Multiply -160000000000000 times -\frac{21}{1000}.

$$x=\frac{0±\sqrt{3360000000000}}{2\times 40000000000000}$$

Take the square root of 3360000000000.

$$x=\frac{0±400000\sqrt{21}}{2\times 40000000000000}$$

Multiply 2 times 40000000000000.

$$x=\frac{0±400000\sqrt{21}}{80000000000000}$$

Now solve the equation x=\frac{0±400000\sqrt{21}}{80000000000000} when ± is plus.

$$x=\frac{\sqrt{21}}{200000000}$$

Now solve the equation x=\frac{0±400000\sqrt{21}}{80000000000000} when ± is minus.

$$x=-\frac{\sqrt{21}}{200000000}$$

The equation is now solved.

$$x=\frac{\sqrt{21}}{200000000} x=-\frac{\sqrt{21}}{200000000}$$