Basic Math Examples

$40^{2} + 550^{2} - 2 \cdot 40 \cdot 550 \cos (45)$

Step 1

Simplify each term.

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Step 1.1

Raise $40$ to the power of $2$ .

$1600 + 550^{2} - 2 \cdot 40 \cdot (550 \cos (45))$

Step 1.2

Raise $550$ to the power of $2$ .

$1600 + 302500 - 2 \cdot 40 \cdot (550 \cos (45))$

Step 1.3

Multiply $- 2$ by $40$ .

$1600 + 302500 - 80 \cdot (550 \cos (45))$

Step 1.4

The exact value of $\cos (45)$ is $\frac{\sqrt{2}}{2}$ .

$1600 + 302500 - 80 \cdot (550 \frac{\sqrt{2}}{2})$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Factor $2$ out of $550$ .

$1600 + 302500 - 80 \cdot (2 (275) \frac{\sqrt{2}}{2})$

Step 1.5.2

Cancel the common factor.

$1600 + 302500 - 80 \cdot (2 \cdot 275 \frac{\sqrt{2}}{2})$

Step 1.5.3

Rewrite the expression.

$1600 + 302500 - 80 \cdot (275 \sqrt{2})$

Step 1.6

Multiply $275$ by $- 80$ .

$1600 + 302500 - 22000 \sqrt{2}$

Step 2

Add $1600$ and $302500$ .

$304100 - 22000 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$304100 - 22000 \sqrt{2}$

Decimal Form:

$272987.30162779 \dots$