Find the Roots (Zeros) f(x)=-1/2(x^3-2.7x-3.1pi)

$f (x) = - \frac{1}{2} (x^{3} - 2.7 x - 3.1 π)$

Set $- \frac{1}{2} \cdot (x^{3} - 2.7 x - 3.1 π)$ equal to $0$ .

$- \frac{1}{2} \cdot (x^{3} - 2.7 x - 3.1 π) = 0$

Solve for $x$ .

Simplify $- \frac{1}{2} \cdot (x^{3} - 2.7 x - 3.1 π)$ .

Multiply $- 3.1$ by $π$ .

$- \frac{1}{2} \cdot (x^{3} - 2.7 x - 9.73893722) = 0$

Apply the distributive property.

$- \frac{1}{2} x^{3} - \frac{1}{2} (- 2.7 x) - \frac{1}{2} \cdot - 9.73893722 = 0$

Simplify.

Combine $x^{3}$ and $\frac{1}{2}$ .

$- \frac{x^{3}}{2} - \frac{1}{2} (- 2.7 x) - \frac{1}{2} \cdot - 9.73893722 = 0$

Multiply $- \frac{1}{2} (- 2.7 x)$ .

Multiply $- 2.7$ by $- 1$ .

$- \frac{x^{3}}{2} + 2.7 (\frac{1}{2}) x - \frac{1}{2} \cdot - 9.73893722 = 0$

Combine $2.7$ and $\frac{1}{2}$ .

$- \frac{x^{3}}{2} + \frac{2.7}{2} x - \frac{1}{2} \cdot - 9.73893722 = 0$

Combine $\frac{2.7}{2}$ and $x$ .

$- \frac{x^{3}}{2} + \frac{2.7 x}{2} - \frac{1}{2} \cdot - 9.73893722 = 0$

Multiply $- \frac{1}{2} \cdot - 9.73893722$ .

Multiply $- 9.73893722$ by $- 1$ .

$- \frac{x^{3}}{2} + \frac{2.7 x}{2} + 9.73893722 (\frac{1}{2}) = 0$

Combine $9.73893722$ and $\frac{1}{2}$ .

$- \frac{x^{3}}{2} + \frac{2.7 x}{2} + \frac{9.73893722}{2} = 0$

Simplify each term.

Factor $2.7$ out of $2.7 x$ .

$- \frac{x^{3}}{2} + \frac{2.7 (x)}{2} + \frac{9.73893722}{2} = 0$

Factor $2$ out of $2$ .

$- \frac{x^{3}}{2} + \frac{2.7 (x)}{2 (1)} + \frac{9.73893722}{2} = 0$

Separate fractions.

$- \frac{x^{3}}{2} + \frac{2.7}{2} \cdot \frac{x}{1} + \frac{9.73893722}{2} = 0$

Divide $2.7$ by $2$ .

$- \frac{x^{3}}{2} + 1.35 \frac{x}{1} + \frac{9.73893722}{2} = 0$

Divide $x$ by $1$ .

$- \frac{x^{3}}{2} + 1.35 x + \frac{9.73893722}{2} = 0$

Divide $9.73893722$ by $2$ .

$- \frac{x^{3}}{2} + 1.35 x + 4.86946861 = 0$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 2.55252942$