Solve frac{sin25^{circ}cos65^{circ}+cos25^{circ}sin65^{circ}}{csc^220^circ-tan^270^circ}=x+1131

$$\frac { \sin 25 ^ { \circ } \cos 65 ^ { \circ } + \cos 25 ^ { \circ } \sin 65 ^ { \circ } } { \csc ^ { 2 } 20 ^ { \circ } - \tan ^ { 2 } 70 ^ { \circ } } = x + 1131$$

Solve for x

$$x = -\frac{2825000000000016296211433671222592191}{2500000000000014408428739915218000} = -1130\frac{4.467570830351532 \times 10^{20}}{2.500000000000014 \times 10^{33}} \approx -1130$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{0.42261826174069944 \cdot 0.42261826174069944 + 0.9063077870366499 \cdot 0.9063077870366499}{2.9238044001630876 ^ {2} - 2.7474774194546216 ^ {2}} = x + 1131$$

Multiply 0.42261826174069944 and 0.42261826174069944 to get 0.1786061951567303400615833404163136.

$$\frac{0.1786061951567303400615833404163136+0.9063077870366499\times 0.9063077870366499}{2.9238044001630876^{2}-2.7474774194546216^{2}}=x+1131$$

Multiply 0.9063077870366499 and 0.9063077870366499 to get 0.82139380484326954852688581517001.

$$\frac{0.1786061951567303400615833404163136+0.82139380484326954852688581517001}{2.9238044001630876^{2}-2.7474774194546216^{2}}=x+1131$$

Add 0.1786061951567303400615833404163136 and 0.82139380484326954852688581517001 to get 0.9999999999999998885884691555863236.

$$\frac{0.9999999999999998885884691555863236}{2.9238044001630876^{2}-2.7474774194546216^{2}}=x+1131$$

Calculate 2.9238044001630876 to the power of 2 and get 8.54863217041303248495747756527376.

$$\frac{0.9999999999999998885884691555863236}{8.54863217041303248495747756527376-2.7474774194546216^{2}}=x+1131$$

Calculate 2.7474774194546216 to the power of 2 and get 7.54863217041302672158598159918656.

$$\frac{0.9999999999999998885884691555863236}{8.54863217041303248495747756527376-7.54863217041302672158598159918656}=x+1131$$

Subtract 7.54863217041302672158598159918656 from 8.54863217041303248495747756527376 to get 1.0000000000000057633714959660872.

$$\frac{0.9999999999999998885884691555863236}{1.0000000000000057633714959660872}=x+1131$$

Expand \frac{0.9999999999999998885884691555863236}{1.0000000000000057633714959660872} by multiplying both numerator and the denominator by 10000000000000000000000000000000000.

$$\frac{9999999999999998885884691555863236}{10000000000000057633714959660872000}=x+1131$$

Reduce the fraction \frac{9999999999999998885884691555863236}{10000000000000057633714959660872000} to lowest terms by extracting and canceling out 4.

$$\frac{2499999999999999721471172888965809}{2500000000000014408428739915218000}=x+1131$$

Swap sides so that all variable terms are on the left hand side.

$$x+1131=\frac{2499999999999999721471172888965809}{2500000000000014408428739915218000}$$

Subtract 1131 from both sides.

$$x=\frac{2499999999999999721471172888965809}{2500000000000014408428739915218000}-1131$$

Convert 1131 to fraction \frac{2827500000000016295932904844111558000}{2500000000000014408428739915218000}.

$$x=\frac{2499999999999999721471172888965809}{2500000000000014408428739915218000}-\frac{2827500000000016295932904844111558000}{2500000000000014408428739915218000}$$

Since \frac{2499999999999999721471172888965809}{2500000000000014408428739915218000} and \frac{2827500000000016295932904844111558000}{2500000000000014408428739915218000} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{2499999999999999721471172888965809-2827500000000016295932904844111558000}{2500000000000014408428739915218000}$$

Subtract 2827500000000016295932904844111558000 from 2499999999999999721471172888965809 to get -2825000000000016296211433671222592191.

$$x=-\frac{2825000000000016296211433671222592191}{2500000000000014408428739915218000}$$