Precalculus Examples

$x^{3} + {(x + 3)}^{3} = 35000$

Step 1

Simplify $x^{3} + {(x + 3)}^{3}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Use the Binomial Theorem.

$x^{3} + x^{3} + 3 x^{2} \cdot 3 + 3 x \cdot 3^{2} + 3^{3} = 35000$

Step 1.1.2

Simplify each term.

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Step 1.1.2.1

Multiply $3$ by $3$ .

$x^{3} + x^{3} + 9 x^{2} + 3 x \cdot 3^{2} + 3^{3} = 35000$

Step 1.1.2.2

Multiply $3$ by $3^{2}$ by adding the exponents.

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Step 1.1.2.2.1

Move $3^{2}$ .

$x^{3} + x^{3} + 9 x^{2} + 3^{2} \cdot 3 x + 3^{3} = 35000$

Step 1.1.2.2.2

Multiply $3^{2}$ by $3$ .

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Step 1.1.2.2.2.1

Raise $3$ to the power of $1$ .

$x^{3} + x^{3} + 9 x^{2} + 3^{2} \cdot 3^{1} x + 3^{3} = 35000$

Step 1.1.2.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{3} + x^{3} + 9 x^{2} + 3^{2 + 1} x + 3^{3} = 35000$

Step 1.1.2.2.3

Add $2$ and $1$ .

$x^{3} + x^{3} + 9 x^{2} + 3^{3} x + 3^{3} = 35000$

Step 1.1.2.3

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

$x^{3} + x^{3} + 9 x^{2} + 27 x + 3^{3} = 35000$

Step 1.1.2.4

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

$x^{3} + x^{3} + 9 x^{2} + 27 x + 27 = 35000$

Step 1.2

Add $x^{3}$ and $x^{3}$ .

$2 x^{3} + 9 x^{2} + 27 x + 27 = 35000$

Step 2

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

$x \approx 24.37580727$

Step 3