Finite Math Examples

${(u + 10)}^{3} + 81 = 0$

Step 1

Simplify ${(u + 10)}^{3} + 81$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Use the Binomial Theorem.

$u^{3} + 3 u^{2} \cdot 10 + 3 u \cdot 10^{2} + 10^{3} + 81 = 0$

Step 1.1.2

Simplify each term.

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Step 1.1.2.1

Multiply $10$ by $3$ .

$u^{3} + 30 u^{2} + 3 u \cdot 10^{2} + 10^{3} + 81 = 0$

Step 1.1.2.2

Raise $10$ to the power of $2$ .

$u^{3} + 30 u^{2} + 3 u \cdot 100 + 10^{3} + 81 = 0$

Step 1.1.2.3

Multiply $100$ by $3$ .

$u^{3} + 30 u^{2} + 300 u + 10^{3} + 81 = 0$

Step 1.1.2.4

Raise $10$ to the power of $3$ .

$u^{3} + 30 u^{2} + 300 u + 1000 + 81 = 0$

Step 1.2

Add $1000$ and $81$ .

$u^{3} + 30 u^{2} + 300 u + 1081 = 0$

Step 2

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

$u \approx - 14.32674871$

Step 3