Finite Math Examples

${(u - 1)}^{3} + 80 = 0$

Step 1

Subtract $80$ from both sides of the equation.

${(u - 1)}^{3} = - 80$

Step 2

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

$u - 1 = \sqrt[3]{- 80}$

Step 3

Simplify $\sqrt[3]{- 80}$ .

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Step 3.1

Rewrite $- 80$ as ${(- 2)}^{3} \cdot 10$ .

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Step 3.1.1

Factor $- 8$ out of $- 80$ .

$u - 1 = \sqrt[3]{- 8 (10)}$

Step 3.1.2

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

$u - 1 = \sqrt[3]{{(- 2)}^{3} \cdot 10}$

Step 3.2

Pull terms out from under the radical.

$u - 1 = - 2 \sqrt[3]{10}$

Step 4

Add $1$ to both sides of the equation.

$u = - 2 \sqrt[3]{10} + 1$

Step 5

The result can be shown in multiple forms.

Exact Form:

$u = - 2 \sqrt[3]{10} + 1$

Decimal Form:

$u = - 3.30886938 \dots$

Step 6