Calculus Examples

$1536 - 960 + 3 + x \sqrt{383 - 5} x \sqrt{283} + \sqrt{83}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Move $x$ .

$1536 - 960 + 3 + x \cdot x \sqrt{383 - 5} \sqrt{283} + \sqrt{83}$

Step 1.1.2

Multiply $x$ by $x$ .

$1536 - 960 + 3 + x^{2} \sqrt{383 - 5} \sqrt{283} + \sqrt{83}$

Step 1.2

Subtract $5$ from $383$ .

$1536 - 960 + 3 + x^{2} \sqrt{378} \sqrt{283} + \sqrt{83}$

Step 1.3

Rewrite $378$ as $3^{2} \cdot 42$ .

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Step 1.3.1

Factor $9$ out of $378$ .

$1536 - 960 + 3 + x^{2} \sqrt{9 (42)} \sqrt{283} + \sqrt{83}$

Step 1.3.2

Rewrite $9$ as $3^{2}$ .

$1536 - 960 + 3 + x^{2} \sqrt{3^{2} \cdot 42} \sqrt{283} + \sqrt{83}$

Step 1.4

Pull terms out from under the radical.

$1536 - 960 + 3 + x^{2} (3 \sqrt{42}) \sqrt{283} + \sqrt{83}$

Step 1.5

Move $3$ to the left of $x^{2}$ .

$1536 - 960 + 3 + 3 \cdot x^{2} \sqrt{42} \sqrt{283} + \sqrt{83}$

Step 1.6

Multiply $3 x^{2} \sqrt{42} \sqrt{283}$ .

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Step 1.6.1

Combine using the product rule for radicals.

$1536 - 960 + 3 + 3 x^{2} \sqrt{283 \cdot 42} + \sqrt{83}$

Step 1.6.2

Multiply $283$ by $42$ .

$1536 - 960 + 3 + 3 x^{2} \sqrt{11886} + \sqrt{83}$

Step 2

Simplify the expression.

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Step 2.1

Subtract $960$ from $1536$ .

$576 + 3 + 3 x^{2} \sqrt{11886} + \sqrt{83}$

Step 2.2

Add $576$ and $3$ .

$579 + 3 x^{2} \sqrt{11886} + \sqrt{83}$

Step 2.3

Reorder $579$ and $3 x^{2} \sqrt{11886}$ .

$3 x^{2} \sqrt{11886} + 579 + \sqrt{83}$