Finite Math Examples

$2 t^{3} + 4 = 50$

Step 1

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

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Step 1.1

Subtract $4$ from both sides of the equation.

$2 t^{3} = 50 - 4$

Step 1.2

Subtract $4$ from $50$ .

$2 t^{3} = 46$

Step 2

Subtract $46$ from both sides of the equation.

$2 t^{3} - 46 = 0$

Step 3

Factor $2$ out of $2 t^{3} - 46$ .

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Step 3.1

Factor $2$ out of $2 t^{3}$ .

$2 (t^{3}) - 46 = 0$

Step 3.2

Factor $2$ out of $- 46$ .

$2 t^{3} + 2 \cdot - 23 = 0$

Step 3.3

Factor $2$ out of $2 t^{3} + 2 \cdot - 23$ .

$2 (t^{3} - 23) = 0$

Step 4

Divide each term in $2 (t^{3} - 23) = 0$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 (t^{3} - 23) = 0$ by $2$ .

$\frac{2 (t^{3} - 23)}{2} = \frac{0}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 (t^{3} - 23)}{2} = \frac{0}{2}$

Step 4.2.1.2

Divide $t^{3} - 23$ by $1$ .

$t^{3} - 23 = \frac{0}{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $2$ .

$t^{3} - 23 = 0$

Step 5

Add $23$ to both sides of the equation.

$t^{3} = 23$

Step 6

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

$t = \sqrt[3]{23}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$t = \sqrt[3]{23}$

Decimal Form:

$t = 2.84386697 \dots$