Basic Math Examples

${(u - 10)}^{3} + 48 = 0$

Step 1

Subtract $48$ from both sides of the equation.

${(u - 10)}^{3} = - 48$

Step 2

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

$u - 10 = \sqrt[3]{- 48}$

Step 3

Simplify $\sqrt[3]{- 48}$ .

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Step 3.1

Rewrite $- 48$ as ${(- 2)}^{3} \cdot 6$ .

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Step 3.1.1

Factor $- 8$ out of $- 48$ .

$u - 10 = \sqrt[3]{- 8 (6)}$

Step 3.1.2

Rewrite $- 8$ as ${(- 2)}^{3}$ .

$u - 10 = \sqrt[3]{{(- 2)}^{3} \cdot 6}$

Step 3.2

Pull terms out from under the radical.

$u - 10 = - 2 \sqrt[3]{6}$

Step 4

Add $10$ to both sides of the equation.

$u = - 2 \sqrt[3]{6} + 10$

Step 5

The result can be shown in multiple forms.

Exact Form:

$u = - 2 \sqrt[3]{6} + 10$

Decimal Form:

$u = 6.36575881 \dots$