Solve -450^circ+frac{7:7/2-frac{6sqrt{31}}{(2/3)-2}-sqrt{11}}{2}

$$\frac { - 450 ^ { \circ } + \frac { 7 : 7 } { 2 } - \frac { 6 \sqrt { 31 } } { ( \frac { 2 } { 3 } ) - 2 } - \sqrt { 11 } } { 2 }$$

Evaluate

$$\frac{9\sqrt{31}}{4}-\frac{\sqrt{11}}{2}-\frac{899}{4}\approx -213.880842579$$

Solution Steps

Divide 7 by 7 to get 1.

$$\frac{-450+\frac{1}{2}-\frac{6\sqrt{31}}{\frac{2}{3}-2}-\sqrt{11}}{2}$$

Convert -450 to fraction -\frac{900}{2}.

$$\frac{-\frac{900}{2}+\frac{1}{2}-\frac{6\sqrt{31}}{\frac{2}{3}-2}-\sqrt{11}}{2}$$

Since -\frac{900}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-900+1}{2}-\frac{6\sqrt{31}}{\frac{2}{3}-2}-\sqrt{11}}{2}$$

Add -900 and 1 to get -899.

$$\frac{-\frac{899}{2}-\frac{6\sqrt{31}}{\frac{2}{3}-2}-\sqrt{11}}{2}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{-\frac{899}{2}-\frac{6\sqrt{31}}{\frac{2}{3}-\frac{6}{3}}-\sqrt{11}}{2}$$

Since \frac{2}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{899}{2}-\frac{6\sqrt{31}}{\frac{2-6}{3}}-\sqrt{11}}{2}$$

Subtract 6 from 2 to get -4.

$$\frac{-\frac{899}{2}-\frac{6\sqrt{31}}{-\frac{4}{3}}-\sqrt{11}}{2}$$

Divide 6\sqrt{31} by -\frac{4}{3} by multiplying 6\sqrt{31} by the reciprocal of -\frac{4}{3}.

$$\frac{-\frac{899}{2}-\frac{6\sqrt{31}\times 3}{-4}-\sqrt{11}}{2}$$

Multiply 6 and 3 to get 18.

$$\frac{-\frac{899}{2}-\frac{18\sqrt{31}}{-4}-\sqrt{11}}{2}$$

Divide 18\sqrt{31} by -4 to get -\frac{9}{2}\sqrt{31}.

$$\frac{-\frac{899}{2}-\left(-\frac{9}{2}\sqrt{31}\right)-\sqrt{11}}{2}$$

The opposite of -\frac{9}{2}\sqrt{31} is \frac{9}{2}\sqrt{31}.

$$\frac{-\frac{899}{2}+\frac{9}{2}\sqrt{31}-\sqrt{11}}{2}$$

Factor

$$\frac{9 \sqrt{31} - 2 \sqrt{11} - 899}{4} = -213.88084257881016$$