Solve Y=(x/8)^3+x

$$Y = ( \frac { x } { 8 } ) ^ { 3 } + x$$

Solve for Y

$$Y=\frac{x^{3}}{512}+x$$

Short Solution Steps

To raise \frac{x}{8} to a power, raise both numerator and denominator to the power and then divide.

$$Y=\frac{x^{3}}{8^{3}}+x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{8^{3}}{8^{3}}.

$$Y=\frac{x^{3}}{8^{3}}+\frac{x\times 8^{3}}{8^{3}}$$

Since \frac{x^{3}}{8^{3}} and \frac{x\times 8^{3}}{8^{3}} have the same denominator, add them by adding their numerators.

$$Y=\frac{x^{3}+x\times 8^{3}}{8^{3}}$$

Do the multiplications in x^{3}+x\times 8^{3}.

$$Y=\frac{x^{3}+512x}{8^{3}}$$

Calculate 8 to the power of 3 and get 512.

$$Y=\frac{x^{3}+512x}{512}$$

Divide each term of x^{3}+512x by 512 to get \frac{1}{512}x^{3}+x.

$$Y=\frac{1}{512}x^{3}+x$$

Solve for x

$$x=\sqrt[3]{\frac{256\sqrt{81Y^{2}+6144}}{9}+256Y}+\sqrt[3]{-\frac{256\sqrt{81Y^{2}+6144}}{9}+256Y}$$