Solve y=3(x+7)^3

$$y = 3 ( x + 7 ) ^ { 3 }$$

Solve for y

$$y=3\left(x+7\right)^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+7\right)^{3}.

$$y=3\left(x^{3}+21x^{2}+147x+343\right)$$

Use the distributive property to multiply 3 by x^{3}+21x^{2}+147x+343.

$$y=3x^{3}+63x^{2}+441x+1029$$

Solve for x (complex solution)

$$x=\frac{3^{\frac{2}{3}}\sqrt[3]{y}-21}{3}$$

$$x=\frac{3^{\frac{2}{3}}e^{\frac{4\pi i}{3}}\sqrt[3]{y}-21}{3}$$

$$x=\frac{3^{\frac{2}{3}}e^{\frac{2\pi i}{3}}\sqrt[3]{y}-21}{3}$$

Solve for x

$$x=\frac{3^{\frac{2}{3}}\sqrt[3]{y}-21}{3}$$