Calculus Examples

$14 = 2 x (900 + 32 x - x^{2})$

Step 1

Simplify $2 x (900 + 32 x - x^{2})$ .

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Step 1.1

Apply the distributive property.

$14 = 2 x \cdot 900 + 2 x (32 x) + 2 x (- x^{2})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $900$ by $2$ .

$14 = 1800 x + 2 x (32 x) + 2 x (- x^{2})$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$14 = 1800 x + 2 \cdot 32 x \cdot x + 2 x (- x^{2})$

Step 1.2.3

Rewrite using the commutative property of multiplication.

$14 = 1800 x + 2 \cdot 32 x \cdot x + 2 \cdot - 1 x \cdot x^{2}$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $x$ by $x$ by adding the exponents.

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Step 1.3.1.1

Move $x$ .

$14 = 1800 x + 2 \cdot 32 (x \cdot x) + 2 \cdot - 1 x \cdot x^{2}$

Step 1.3.1.2

Multiply $x$ by $x$ .

$14 = 1800 x + 2 \cdot 32 x^{2} + 2 \cdot - 1 x \cdot x^{2}$

Step 1.3.2

Multiply $2$ by $32$ .

$14 = 1800 x + 64 x^{2} + 2 \cdot - 1 x \cdot x^{2}$

Step 1.3.3

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

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Step 1.3.3.1

Move $x^{2}$ .

$14 = 1800 x + 64 x^{2} + 2 \cdot - 1 (x^{2} x)$

Step 1.3.3.2

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

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Step 1.3.3.2.1

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

$14 = 1800 x + 64 x^{2} + 2 \cdot - 1 (x^{2} x^{1})$

Step 1.3.3.2.2

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

$14 = 1800 x + 64 x^{2} + 2 \cdot - 1 x^{2 + 1}$

Step 1.3.3.3

Add $2$ and $1$ .

$14 = 1800 x + 64 x^{2} + 2 \cdot - 1 x^{3}$

Step 1.3.4

Multiply $2$ by $- 1$ .

$14 = 1800 x + 64 x^{2} - 2 x^{3}$

Step 2

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

$x \approx - 18.00571665, 0.00777562$

Step 3