Solve Xquadcos(8.6^circ)cos(180^circ/13)+sqrt{1-x^2}sin(8.6^circ)=0.96

$$X \quad \cos ( 8.6 ^ { \circ } ) \cos ( \frac { 180 ^ { \circ } } { 13 } ) + \sqrt { 1 - x ^ { 2 } } \sin ( 8.6 ^ { \circ } ) = 0.96$$

Solve for X_0

$$X_{0}=\frac{-186919179304636912500000000000\sqrt{1-x^{2}}+1200000000000000000000000000000}{1200031147006732259399221893877}$$

$$|x|\leq 1$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$X 0.9887563810470058 \cdot 0.970941817426052 + \sqrt{1 - x ^ {2}} 0.14953534344370953 = 0.96$$

Multiply 0.9887563810470058 and 0.970941817426052 to get 0.9600249176053858075193775151016.

$$X_{0}\times 0.9600249176053858075193775151016+0.14953534344370953\sqrt{1-x^{2}}=0.96$$

Subtract 0.14953534344370953\sqrt{1-x^{2}} from both sides.

$$X_{0}\times 0.9600249176053858075193775151016=0.96-0.14953534344370953\sqrt{1-x^{2}}$$

The equation is in standard form.

$$0.9600249176053858075193775151016X_{0}=-\frac{14953534344370953\sqrt{1-x^{2}}}{100000000000000000}+0.96$$

Divide both sides of the equation by 0.9600249176053858075193775151016, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.9600249176053858075193775151016X_{0}}{0.9600249176053858075193775151016}=\frac{-\frac{14953534344370953\sqrt{1-x^{2}}}{100000000000000000}+0.96}{0.9600249176053858075193775151016}$$

Dividing by 0.9600249176053858075193775151016 undoes the multiplication by 0.9600249176053858075193775151016.

$$X_{0}=\frac{-\frac{14953534344370953\sqrt{1-x^{2}}}{100000000000000000}+0.96}{0.9600249176053858075193775151016}$$

Divide 0.96-\frac{14953534344370953\sqrt{1-x^{2}}}{100000000000000000} by 0.9600249176053858075193775151016 by multiplying 0.96-\frac{14953534344370953\sqrt{1-x^{2}}}{100000000000000000} by the reciprocal of 0.9600249176053858075193775151016.

$$X_{0}=\frac{-186919179304636912500000000000\sqrt{1-x^{2}}+1200000000000000000000000000000}{1200031147006732259399221893877}$$

Solve for x

$$x=\frac{\sqrt{-\frac{1440074753786293450937544883750075585373479076836738650091129X_{0}^{2}}{8734694897979751061998330864383164062500000000000000000000}+\frac{24576637890697876672496064386600960X_{0}}{74536063129427209062385756709403}-\frac{3996618582494097054583485657720796}{24845354376475736354128585569801}}}{2}$$

$$x=-\frac{\sqrt{-\frac{1440074753786293450937544883750075585373479076836738650091129X_{0}^{2}}{8734694897979751061998330864383164062500000000000000000000}+\frac{24576637890697876672496064386600960X_{0}}{74536063129427209062385756709403}-\frac{3996618582494097054583485657720796}{24845354376475736354128585569801}}}{2}\text{, }X_{0}\geq \frac{1013080820695363087500000000000}{1200031147006732259399221893877}\text{ and }-\frac{1200031147006732259399221893877X_{0}}{186919179304636912500000000000}+\frac{32000000000000000}{4984511448123651}\geq 0$$