Solve (27/30)^3=(3.8*10^5/a)^2

$$( \frac { 27 } { 30 } ) ^ { 3 } = ( \frac { 3.8 \times 10 ^ { 5 } } { a } ) ^ { 2 }$$

Solve for a

$$a = -\frac{3800000 \sqrt{10}}{27} \approx -445061.300319994$$

$$a = \frac{3800000 \sqrt{10}}{27} \approx 445061.300319994$$

Steps by Finding Square Root

Reduce the fraction \frac{27}{30} to lowest terms by extracting and canceling out 3.

$$\left(\frac{9}{10}\right)^{3}=\left(\frac{3.8\times 10^{5}}{a}\right)^{2}$$

Calculate \frac{9}{10} to the power of 3 and get \frac{729}{1000}.

$$\frac{729}{1000}=\left(\frac{3.8\times 10^{5}}{a}\right)^{2}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{729}{1000}=\left(\frac{3.8\times 100000}{a}\right)^{2}$$

Multiply 3.8 and 100000 to get 380000.

$$\frac{729}{1000}=\left(\frac{380000}{a}\right)^{2}$$

To raise \frac{380000}{a} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{729}{1000}=\frac{380000^{2}}{a^{2}}$$

Calculate 380000 to the power of 2 and get 144400000000.

$$\frac{729}{1000}=\frac{144400000000}{a^{2}}$$

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

$$\frac{144400000000}{a^{2}}=\frac{729}{1000}$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 1000a^{2}, the least common multiple of a^{2},1000.

$$1000\times 144400000000=729a^{2}$$

Multiply 1000 and 144400000000 to get 144400000000000.

$$144400000000000=729a^{2}$$

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

$$729a^{2}=144400000000000$$

Divide both sides by 729.

$$a^{2}=\frac{144400000000000}{729}$$

Take the square root of both sides of the equation.

$$a=\frac{3800000\sqrt{10}}{27} a=-\frac{3800000\sqrt{10}}{27}$$

Steps Using the Quadratic Formula

Reduce the fraction \frac{27}{30} to lowest terms by extracting and canceling out 3.

$$\left(\frac{9}{10}\right)^{3}=\left(\frac{3.8\times 10^{5}}{a}\right)^{2}$$

Calculate \frac{9}{10} to the power of 3 and get \frac{729}{1000}.

$$\frac{729}{1000}=\left(\frac{3.8\times 10^{5}}{a}\right)^{2}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{729}{1000}=\left(\frac{3.8\times 100000}{a}\right)^{2}$$

Multiply 3.8 and 100000 to get 380000.

$$\frac{729}{1000}=\left(\frac{380000}{a}\right)^{2}$$

To raise \frac{380000}{a} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{729}{1000}=\frac{380000^{2}}{a^{2}}$$

Calculate 380000 to the power of 2 and get 144400000000.

$$\frac{729}{1000}=\frac{144400000000}{a^{2}}$$

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

$$\frac{144400000000}{a^{2}}=\frac{729}{1000}$$

Subtract \frac{729}{1000} from both sides.

$$\frac{144400000000}{a^{2}}-\frac{729}{1000}=0$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a^{2} and 1000 is 1000a^{2}. Multiply \frac{144400000000}{a^{2}} times \frac{1000}{1000}. Multiply \frac{729}{1000} times \frac{a^{2}}{a^{2}}.

$$\frac{144400000000\times 1000}{1000a^{2}}-\frac{729a^{2}}{1000a^{2}}=0$$

Since \frac{144400000000\times 1000}{1000a^{2}} and \frac{729a^{2}}{1000a^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{144400000000\times 1000-729a^{2}}{1000a^{2}}=0$$

Do the multiplications in 144400000000\times 1000-729a^{2}.

$$\frac{144400000000000-729a^{2}}{1000a^{2}}=0$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 1000a^{2}.

$$144400000000000-729a^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-729a^{2}[phone]=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -729 for a, 0 for b, and 144400000000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-729\right)\times 144400000000000}}{2\left(-729\right)}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-729\right)\times 144400000000000}}{2\left(-729\right)}$$

Multiply -4 times -729.

$$a=\frac{0±\sqrt{2916\times 144400000000000}}{2\left(-729\right)}$$

Multiply 2916 times 144400000000000.

$$a=\frac{0±\sqrt{421070400000000000}}{2\left(-729\right)}$$

Take the square root of 421070400000000000.

$$a=\frac{0±205200000\sqrt{10}}{2\left(-729\right)}$$

Multiply 2 times -729.

$$a=\frac{0±205200000\sqrt{10}}{-1458}$$

Now solve the equation a=\frac{0±205200000\sqrt{10}}{-1458} when ± is plus.

$$a=-\frac{3800000\sqrt{10}}{27}$$

Now solve the equation a=\frac{0±205200000\sqrt{10}}{-1458} when ± is minus.

$$a=\frac{3800000\sqrt{10}}{27}$$

The equation is now solved.

$$a=-\frac{3800000\sqrt{10}}{27} a=\frac{3800000\sqrt{10}}{27}$$