Solve -18-2[-12-4]/2sqrt{31+9-41sqrt{4+9+54}}

$$\frac { - 18 - 2 [ - 12 - 4 ] } { 2 \sqrt { 31 + 9 - 41 } \sqrt { 4 + 9 + 54 } }$$

Evaluate (complex solution)

$$-\frac{7\sqrt{67}i}{67}\approx -0-0.85518611i$$

Solution Steps

Subtract 4 from -12 to get -16.

$$\frac{-18-2\left(-16\right)}{2\sqrt{31+9-41}\sqrt{4+9+54}}$$

Multiply 2 and -16 to get -32.

$$\frac{-18-\left(-32\right)}{2\sqrt{31+9-41}\sqrt{4+9+54}}$$

The opposite of -32 is 32.

$$\frac{-18+32}{2\sqrt{31+9-41}\sqrt{4+9+54}}$$

Add -18 and 32 to get 14.

$$\frac{14}{2\sqrt{31+9-41}\sqrt{4+9+54}}$$

Add 31 and 9 to get 40.

$$\frac{14}{2\sqrt{40-41}\sqrt{4+9+54}}$$

Subtract 41 from 40 to get -1.

$$\frac{14}{2\sqrt{-1}\sqrt{4+9+54}}$$

Calculate the square root of -1 and get i.

$$\frac{14}{2i\sqrt{4+9+54}}$$

Add 4 and 9 to get 13.

$$\frac{14}{2i\sqrt{13+54}}$$

Add 13 and 54 to get 67.

$$\frac{14}{2i\sqrt{67}}$$

Rationalize the denominator of \frac{14}{2i\sqrt{67}} by multiplying numerator and denominator by \sqrt{67}.

$$\frac{14\sqrt{67}}{2i\left(\sqrt{67}\right)^{2}}$$

The square of \sqrt{67} is 67.

$$\frac{14\sqrt{67}}{2i\times 67}$$

Multiply 2i and 67 to get 134i.

$$\frac{14\sqrt{67}}{134i}$$

Divide 14\sqrt{67} by 134i to get -\frac{7}{67}i\sqrt{67}.

$$-\frac{7}{67}i\sqrt{67}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$