Solve left(3.8*10^8right)^3/27.3^2=frac{{left(1.43*10^12right)}^3}{{x}^2}

$$\frac{ { \left(3.8 \times { 10 }^{ 8 } \right) }^{ 3 } }{ { 27.3 }^{ 2 } } = \frac{ { \left(1.43 \times { 10 }^{ 12 } \right) }^{ 3 } }{ { x }^{ 2 } }$$

Solve for x

$$x = \frac{19519500 \sqrt{13585}}{361} \approx 6302187.330774317$$

$$x = -\frac{19519500 \sqrt{13585}}{361} \approx -6302187.330774317$$

Steps by Finding Square Root

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

$$\frac{100}{74529}x^{2}\times \left(3.8\times 10^{8}\right)^{3}=\left(1.43\times 10^{12}\right)^{3}$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{100}{74529}x^{2}\times \left(3.8\times 100000000\right)^{3}=\left(1.43\times 10^{12}\right)^{3}$$

Multiply 3.8 and 100000000 to get 380000000.

$$\frac{100}{74529}x^{2}\times 380000000^{3}=\left(1.43\times 10^{12}\right)^{3}$$

Calculate 380000000 to the power of 3 and get 54872000000000000000000000.

$$\frac{100}{74529}x^{2}\times 54872000000000000000000000=\left(1.43\times 10^{12}\right)^{3}$$

Multiply \frac{100}{74529} and 54872000000000000000000000 to get \frac{5487200000000000000000000000}{74529}.

$$\frac{5487200000000000000000000000}{74529}x^{2}=\left(1.43\times 10^{12}\right)^{3}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$\frac{5487200000000000000000000000}{74529}x^{2}=\left(1.43\times 1000000000000\right)^{3}$$

Multiply 1.43 and 1000000000000 to get 1430000000000.

$$\frac{5487200000000000000000000000}{74529}x^{2}=1430000000000^{3}$$

Calculate 1430000000000 to the power of 3 and get 2924207000000000000000000000000000000.

$$\frac{5487200000000000000000000000}{74529}x^{2}=2924207000000000000000000000000000000$$

Divide both sides by \frac{5487200000000000000000000000}{74529}.

$$x^{2}=\frac{2924207000000000000000000000000000000}{\frac{5487200000000000000000000000}{74529}}$$

Take the square root of both sides of the equation.

$$x=\frac{19519500\sqrt{13585}}{361} x=-\frac{19519500\sqrt{13585}}{361}$$

Steps Using the Quadratic Formula

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

$$\frac{100}{74529}x^{2}\times \left(3.8\times 10^{8}\right)^{3}=\left(1.43\times 10^{12}\right)^{3}$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{100}{74529}x^{2}\times \left(3.8\times 100000000\right)^{3}=\left(1.43\times 10^{12}\right)^{3}$$

Multiply 3.8 and 100000000 to get 380000000.

$$\frac{100}{74529}x^{2}\times 380000000^{3}=\left(1.43\times 10^{12}\right)^{3}$$

Calculate 380000000 to the power of 3 and get 54872000000000000000000000.

$$\frac{100}{74529}x^{2}\times 54872000000000000000000000=\left(1.43\times 10^{12}\right)^{3}$$

Multiply \frac{100}{74529} and 54872000000000000000000000 to get \frac{5487200000000000000000000000}{74529}.

$$\frac{5487200000000000000000000000}{74529}x^{2}=\left(1.43\times 10^{12}\right)^{3}$$

Calculate 10 to the power of 12 and get 1000000000000.

$$\frac{5487200000000000000000000000}{74529}x^{2}=\left(1.43\times 1000000000000\right)^{3}$$

Multiply 1.43 and 1000000000000 to get 1430000000000.

$$\frac{5487200000000000000000000000}{74529}x^{2}=1430000000000^{3}$$

Calculate 1430000000000 to the power of 3 and get 2924207000000000000000000000000000000.

$$\frac{5487200000000000000000000000}{74529}x^{2}=2924207000000000000000000000000000000$$

Subtract 2924207000000000000000000000000000000 from both sides.

$$\frac{5487200000000000000000000000}{74529}x^{2}-2924207000000000000000000000000000000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{5487200000000000000000000000}{74529} for a, 0 for b, and -2924207000000000000000000000000000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{5487200000000000000000000000}{74529}\left(-2924207000000000000000000000000000000\right)}}{2\times \frac{5487200000000000000000000000}{74529}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{5487200000000000000000000000}{74529}\left(-2924207000000000000000000000000000000\right)}}{2\times \frac{5487200000000000000000000000}{74529}}$$

Multiply -4 times \frac{5487200000000000000000000000}{74529}.

$$x=\frac{0±\sqrt{-\frac{21948800000000000000000000000}{74529}\left(-2924207000000000000000000000000000000\right)}}{2\times \frac{5487200000000000000000000000}{74529}}$$

Multiply -\frac{21948800000000000000000000000}{74529} times -2924207000000000000000000000000000000.

$$x=\frac{0±\sqrt{\frac{379780086400000000000000000000000000000000000000000000000000000}{441}}}{2\times \frac{5487200000000000000000000000}{74529}}$$

Take the square root of \frac{379780086400000000000000000000000000000000000000000000000000000}{441}.

$$x=\frac{0±\frac{167200000000000000000000000000\sqrt{13585}}{21}}{2\times \frac{5487200000000000000000000000}{74529}}$$

Multiply 2 times \frac{5487200000000000000000000000}{74529}.

$$x=\frac{0±\frac{167200000000000000000000000000\sqrt{13585}}{21}}{\frac{10974400000000000000000000000}{74529}}$$

Now solve the equation x=\frac{0±\frac{167200000000000000000000000000\sqrt{13585}}{21}}{\frac{10974400000000000000000000000}{74529}} when ± is plus.

$$x=\frac{19519500\sqrt{13585}}{361}$$

Now solve the equation x=\frac{0±\frac{167200000000000000000000000000\sqrt{13585}}{21}}{\frac{10974400000000000000000000000}{74529}} when ± is minus.

$$x=-\frac{19519500\sqrt{13585}}{361}$$

The equation is now solved.

$$x=\frac{19519500\sqrt{13585}}{361} x=-\frac{19519500\sqrt{13585}}{361}$$