Solve 46/60=x^2+11547^2-2x11547cos(36)

$$\frac{ 46 }{ 60 } = { x }^{ 2 } + { 11547 }^{ 2 } -2x11547 \cos ( 36 )$$

Solve for x_11547

$$x_{11547}=\frac{200000000000000x^{2}}{323606797749979}+\frac{79999924940000000000000}{970820393249937}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{46}{60} = {(x)} ^ {2} + {(11547)} ^ {2} - 2 x 11547 \cdot 0.8090169943749475$$

Reduce the fraction \frac{46}{60} to lowest terms by extracting and canceling out 2.

$$\frac{23}{30}=x^{2}+11547^{2}-2x_{11547}\times 0.8090169943749475$$

Calculate 11547 to the power of 2 and get 133333209.

$$\frac{23}{30}=x^{2}[phone]x_{11547}\times 0.8090169943749475$$

Multiply 2 and 0.8090169943749475 to get 1.618033988749895.

$$\frac{23}{30}=x^{2}[phone]-1.618033988749895x_{11547}$$

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

$$x^{2}[phone]-1.618033988749895x_{11547}=\frac{23}{30}$$

Subtract x^{2} from both sides.

$$133333209-1.618033988749895x_{11547}=\frac{23}{30}-x^{2}$$

Subtract 133333209 from both sides.

$$-1.618033988749895x_{11547}=\frac{23}{30}-x^{2}-133333209$$

Subtract 133333209 from \frac{23}{30} to get -\frac{3999996247}{30}.

$$-1.618033988749895x_{11547}=-\frac{3999996247}{30}-x^{2}$$

The equation is in standard form.

$$-1.618033988749895x_{11547}=-x^{2}-\frac{3999996247}{30}$$

Divide both sides of the equation by -1.618033988749895, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-1.618033988749895x_{11547}}{-1.618033988749895}=\frac{-x^{2}-\frac{3999996247}{30}}{-1.618033988749895}$$

Dividing by -1.618033988749895 undoes the multiplication by -1.618033988749895.

$$x_{11547}=\frac{-x^{2}-\frac{3999996247}{30}}{-1.618033988749895}$$

Divide -\frac{3999996247}{30}-x^{2} by -1.618033988749895 by multiplying -\frac{3999996247}{30}-x^{2} by the reciprocal of -1.618033988749895.

$$x_{11547}=\frac{200000000000000x^{2}}{323606797749979}+\frac{79999924940000000000000}{970820393249937}$$

Solve for x

$$x=\frac{\sqrt{5824922359499622x_{11547}-479999549640000000000000}}{60000000}$$

$$x=-\frac{\sqrt{5824922359499622x_{11547}-479999549640000000000000}}{60000000}\text{, }x_{11547}\geq \frac{79999924940000000000000}{970820393249937}$$