Solve -Y=-0.5(x-10)^3+15

$$- Y = - 0.5 ( x - 10 ) ^ { 3 } + 15$$

Solve for Y

$$Y=\frac{\left(x-10\right)^{3}}{2}-15$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-10\right)^{3}.

$$-Y=-0.5\left(x^{3}-30x^{2}+300x-1000\right)+15$$

Use the distributive property to multiply -0.5 by x^{3}-30x^{2}+300x-1000.

$$-Y=-0.5x^{3}+15x^{2}-150x+500+15$$

Add 500 and 15 to get 515.

$$-Y=-0.5x^{3}+15x^{2}-150x+515$$

The equation is in standard form.

$$-Y=-\frac{x^{3}}{2}+15x^{2}-150x+515$$

Divide both sides by -1.

$$\frac{-Y}{-1}=\frac{-\frac{x^{3}}{2}+15x^{2}-150x+515}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$Y=\frac{-\frac{x^{3}}{2}+15x^{2}-150x+515}{-1}$$

Divide -\frac{x^{3}}{2}+15x^{2}-150x+515 by -1.

$$Y=\frac{x^{3}}{2}-15x^{2}+150x-515$$

Solve for x (complex solution)

$$x=\sqrt[3]{2\left(Y+15\right)}+10$$

$$x=e^{\frac{i\times 4\pi }{3}}\sqrt[3]{2\left(Y+15\right)}+10$$

$$x=e^{\frac{i\times 2\pi }{3}}\sqrt[3]{2\left(Y+15\right)}+10$$

Solve for x

$$x=\sqrt[3]{2\left(Y+15\right)}+10$$