Solve for w w=33-((10.45+10 square root of 9-9)(33-10))/22

$w = 33 - \frac{(10.45 + 10 \sqrt{9} - 9) (33 - 10)}{22}$

Step 1

Simplify each term.

Simplify the numerator.

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

$w = 33 - \frac{(10.45 + 10 \sqrt{3^{2}} - 9) (33 - 10)}{22}$

Pull terms out from under the radical, assuming positive real numbers.

$w = 33 - \frac{(10.45 + 10 \cdot 3 - 9) (33 - 10)}{22}$

Multiply $10$ by $3$ .

$w = 33 - \frac{(10.45 + 30 - 9) (33 - 10)}{22}$

Add $10.45$ and $30$ .

$w = 33 - \frac{(40.45 - 9) (33 - 10)}{22}$

Subtract $9$ from $40.45$ .

$w = 33 - \frac{31.45 (33 - 10)}{22}$

Subtract $10$ from $33$ .

$w = 33 - \frac{31.45 \cdot 23}{22}$

Multiply $31.45$ by $23$ .

$w = 33 - \frac{723.35}{22}$

Divide $723.35$ by $22$ .

$w = 33 - 1 \cdot 32.879\overline{54}$

Multiply $- 1$ by $32.879\overline{54}$ .

$w = 33 - 32.879\overline{54}$

Step 2

Subtract $32.879\overline{54}$ from $33$ .

$w = 0.120\overline{45}$