Solve y=0.05(x-40)^3+30

$$y = 0.05 ( x - 40 ) ^ { 3 } + 30$$

Solve for y

$$y=\frac{\left(x-40\right)^{3}}{20}+30$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-40\right)^{3}.

$$y=0.05\left(x^{3}-120x^{2}+4800x-64000\right)+30$$

Use the distributive property to multiply 0.05 by x^{3}-120x^{2}+4800x-64000.

$$y=0.05x^{3}-6x^{2}+240x-3200+30$$

Add -3200 and 30 to get -3170.

$$y=0.05x^{3}-6x^{2}+240x-3170$$

Solve for x (complex solution)

$$x=\sqrt[3]{20\left(y-30\right)}+40$$

$$x=e^{\frac{i\times 4\pi }{3}}\sqrt[3]{20\left(y-30\right)}+40$$

$$x=e^{\frac{i\times 2\pi }{3}}\sqrt[3]{20\left(y-30\right)}+40$$

Solve for x

$$x=\sqrt[3]{20\left(y-30\right)}+40$$