Solve y=1/4(x-40)^3+30

$$y = \frac { 1 } { 4 } ( x - 40 ) ^ { 3 } + 30$$

Solve for y

$$y=\frac{\left(x-40\right)^{3}+120}{4}$$

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}.

$$y=\frac{1}{4}\left(x^{3}-120x^{2}+4800x-64000\right)+30$$

Use the distributive property to multiply \frac{1}{4} by x^{3}-120x^{2}+4800x-64000.

$$y=\frac{1}{4}x^{3}-30x^{2}+1200x-16000+30$$

Add -16000 and 30 to get -15970.

$$y=\frac{1}{4}x^{3}-30x^{2}+1200x-15970$$

Solve for x

$$x=2^{\frac{2}{3}}\sqrt[3]{y-30}+40$$