Solve (150000000000)^3/(31600000)^2=380000000/x^2

$$\frac { ( 150000000000 ) ^ { 3 } } { ( 31600000 ) ^ { 2 } } = \frac { 380000000 } { x ^ { 2 } }$$

Solve for x

$$x=\frac{79\sqrt{57}}{56250000}\approx 0.000010603$$

$$x=-\frac{79\sqrt{57}}{56250000}\approx -0.000010603$$

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}.

$$\frac{1}{998560000000000}x^{2}\times 150000000000^{3}=380000000$$

Calculate 150000000000 to the power of 3 and get 3375000000000000000000000000000000.

$$\frac{1}{998560000000000}x^{2}\times 3375000000000000000000000000000000=380000000$$

Multiply \frac{1}{998560000000000} and 3375000000000000000000000000000000 to get \frac{21093750000000000000000}{6241}.

$$\frac{21093750000000000000000}{6241}x^{2}=380000000$$

Multiply both sides by \frac{6241}{21093750000000000000000}, the reciprocal of \frac{21093750000000000000000}{6241}.

$$x^{2}=380000000\times \frac{6241}{21093750000000000000000}$$

Multiply 380000000 and \frac{6241}{21093750000000000000000} to get \frac{118579}{1054687500000000}.

$$x^{2}=\frac{118579}{1054687500000000}$$

Take the square root of both sides of the equation.

$$x=\frac{79\sqrt{57}}{56250000} x=-\frac{79\sqrt{57}}{56250000}$$

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}.

$$\frac{1}{998560000000000}x^{2}\times 150000000000^{3}=380000000$$

Calculate 150000000000 to the power of 3 and get 3375000000000000000000000000000000.

$$\frac{1}{998560000000000}x^{2}\times 3375000000000000000000000000000000=380000000$$

Multiply \frac{1}{998560000000000} and 3375000000000000000000000000000000 to get \frac{21093750000000000000000}{6241}.

$$\frac{21093750000000000000000}{6241}x^{2}=380000000$$

Subtract 380000000 from both sides.

$$\frac{21093750000000000000000}{6241}x^{2}-380000000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{21093750000000000000000}{6241} for a, 0 for b, and -380000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{21093750000000000000000}{6241}\left(-380000000\right)}}{2\times \frac{21093750000000000000000}{6241}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{21093750000000000000000}{6241}\left(-380000000\right)}}{2\times \frac{21093750000000000000000}{6241}}$$

Multiply -4 times \frac{21093750000000000000000}{6241}.

$$x=\frac{0±\sqrt{-\frac{84375000000000000000000}{6241}\left(-380000000\right)}}{2\times \frac{21093750000000000000000}{6241}}$$

Multiply -\frac{84375000000000000000000}{6241} times -380000000.

$$x=\frac{0±\sqrt{\frac{32062500000000000000000000000000}{6241}}}{2\times \frac{21093750000000000000000}{6241}}$$

Take the square root of \frac{32062500000000000000000000000000}{6241}.

$$x=\frac{0±\frac{750000000000000\sqrt{57}}{79}}{2\times \frac{21093750000000000000000}{6241}}$$

Multiply 2 times \frac{21093750000000000000000}{6241}.

$$x=\frac{0±\frac{750000000000000\sqrt{57}}{79}}{\frac{42187500000000000000000}{6241}}$$

Now solve the equation x=\frac{0±\frac{750000000000000\sqrt{57}}{79}}{\frac{42187500000000000000000}{6241}} when ± is plus.

$$x=\frac{79\sqrt{57}}{56250000}$$

Now solve the equation x=\frac{0±\frac{750000000000000\sqrt{57}}{79}}{\frac{42187500000000000000000}{6241}} when ± is minus.

$$x=-\frac{79\sqrt{57}}{56250000}$$

The equation is now solved.

$$x=\frac{79\sqrt{57}}{56250000} x=-\frac{79\sqrt{57}}{56250000}$$