Solve for x -10-3x^3=-37

$- 10 - 3 x^{3} = - 37$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Add $10$ to both sides of the equation.

$- 3 x^{3} = - 37 + 10$

Add $- 37$ and $10$ .

$- 3 x^{3} = - 27$

Step 2

Add $27$ to both sides of the equation.

$- 3 x^{3} + 27 = 0$

Step 3

Factor $- 3$ out of $- 3 x^{3} + 27$ .

Factor $- 3$ out of $27$ .

$- 3 x^{3} - 3 \cdot - 9 = 0$

Factor $- 3$ out of $- 3 (x^{3}) - 3 (- 9)$ .

$- 3 (x^{3} - 9) = 0$

Step 4

Divide each term in $- 3 (x^{3} - 9) = 0$ by $- 3$ and simplify.

Divide each term in $- 3 (x^{3} - 9) = 0$ by $- 3$ .

$\frac{- 3 (x^{3} - 9)}{- 3} = \frac{0}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 (x^{3} - 9)}{- 3} = \frac{0}{- 3}$

Divide $x^{3} - 9$ by $1$ .

$x^{3} - 9 = \frac{0}{- 3}$

Simplify the right side.

Divide $0$ by $- 3$ .

$x^{3} - 9 = 0$

Step 5

Add $9$ to both sides of the equation.

$x^{3} = 9$

Step 6

Take the cube root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[3]{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt[3]{9}$

Decimal Form:

$x = 2.08008382 \dots$