Solve x^2/24^2=8/6.6^3

$$\frac{ { x }^{ 2 } }{ { 24 }^{ 2 } } = \frac{ 8 }{ { 6.6 }^{ 3 } }$$

Solve for x

$$x = \frac{80 \sqrt{330}}{363} \approx 4.0035046$$

$$x = -\frac{80 \sqrt{330}}{363} \approx -4.0035046$$

Steps by Finding Square Root

Calculate 24 to the power of 2 and get 576.

$$\frac{x^{2}}{576}=\frac{8}{6.6^{3}}$$

Calculate 6.6 to the power of 3 and get 287.496.

$$\frac{x^{2}}{576}=\frac{8}{287.496}$$

Expand \frac{8}{287.496} by multiplying both numerator and the denominator by 1000.

$$\frac{x^{2}}{576}=\frac{8000}{287496}$$

Reduce the fraction \frac{8000}{287496} to lowest terms by extracting and canceling out 8.

$$\frac{x^{2}}{576}=\frac{1000}{35937}$$

Multiply both sides by 576.

$$x^{2}=\frac{1000}{35937}\times 576$$

Multiply \frac{1000}{35937} and 576 to get \frac{64000}{3993}.

$$x^{2}=\frac{64000}{3993}$$

Take the square root of both sides of the equation.

$$x=\frac{80\sqrt{330}}{363} x=-\frac{80\sqrt{330}}{363}$$

Steps Using the Quadratic Formula

Calculate 24 to the power of 2 and get 576.

$$\frac{x^{2}}{576}=\frac{8}{6.6^{3}}$$

Calculate 6.6 to the power of 3 and get 287.496.

$$\frac{x^{2}}{576}=\frac{8}{287.496}$$

Expand \frac{8}{287.496} by multiplying both numerator and the denominator by 1000.

$$\frac{x^{2}}{576}=\frac{8000}{287496}$$

Reduce the fraction \frac{8000}{287496} to lowest terms by extracting and canceling out 8.

$$\frac{x^{2}}{576}=\frac{1000}{35937}$$

Subtract \frac{1000}{35937} from both sides.

$$\frac{x^{2}}{576}-\frac{1000}{35937}=0$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 576 and 35937 is 2299968. Multiply \frac{x^{2}}{576} times \frac{3993}{3993}. Multiply \frac{1000}{35937} times \frac{64}{64}.

$$\frac{3993x^{2}}{2299968}-\frac{1000\times 64}{2299968}=0$$

Since \frac{3993x^{2}}{2299968} and \frac{1000\times 64}{2299968} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3993x^{2}-1000\times 64}{2299968}=0$$

Do the multiplications in 3993x^{2}-1000\times 64.

$$\frac{3993x^{2}-64000}{2299968}=0$$

Divide each term of 3993x^{2}-64000 by 2299968 to get \frac{1}{576}x^{2}-\frac{1000}{35937}.

$$\frac{1}{576}x^{2}-\frac{1000}{35937}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{576} for a, 0 for b, and -\frac{1000}{35937} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{576}\left(-\frac{1000}{35937}\right)}}{2\times \frac{1}{576}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{576}\left(-\frac{1000}{35937}\right)}}{2\times \frac{1}{576}}$$

Multiply -4 times \frac{1}{576}.

$$x=\frac{0±\sqrt{-\frac{1}{144}\left(-\frac{1000}{35937}\right)}}{2\times \frac{1}{576}}$$

Multiply -\frac{1}{144} times -\frac{1000}{35937} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{\frac{125}{646866}}}{2\times \frac{1}{576}}$$

Take the square root of \frac{125}{646866}.

$$x=\frac{0±\frac{5\sqrt{330}}{6534}}{2\times \frac{1}{576}}$$

Multiply 2 times \frac{1}{576}.

$$x=\frac{0±\frac{5\sqrt{330}}{6534}}{\frac{1}{288}}$$

Now solve the equation x=\frac{0±\frac{5\sqrt{330}}{6534}}{\frac{1}{288}} when ± is plus.

$$x=\frac{80\sqrt{330}}{363}$$

Now solve the equation x=\frac{0±\frac{5\sqrt{330}}{6534}}{\frac{1}{288}} when ± is minus.

$$x=-\frac{80\sqrt{330}}{363}$$

The equation is now solved.

$$x=\frac{80\sqrt{330}}{363} x=-\frac{80\sqrt{330}}{363}$$