Solve 46/60=x^2+1.1547^2-2x1.1547cos(36)

$$\frac{ 46 }{ 60 } = { x }^{ 2 } + { 1.1547 }^{ 2 } -2x1.1547 \cos ( 36 )$$

Solve for x_1

$$x_{1}=\frac{2000000000000000000x^{2}}{500619716119217513}+\frac{485713220000000000}{214551306908236077}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$\frac{46}{60} = {(x)} ^ {2} + {(1.1547)} ^ {2} - 2 x 1.1547 \cdot 0.8090169943749475$$

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

$$\frac{23}{30}=x^{2}+1.1547^{2}-2x_{1}\times 0.1547\times 0.8090169943749475$$

Calculate 1.1547 to the power of 2 and get 1.33333209.

$$\frac{23}{30}=x^{2}+1.33333209-2x_{1}\times 0.1547\times 0.8090169943749475$$

Multiply 2 and 0.1547 to get 0.3094.

$$\frac{23}{30}=x^{2}+1.33333209-0.3094x_{1}\times 0.8090169943749475$$

Multiply 0.3094 and 0.8090169943749475 to get 0.2503098580596087565.

$$\frac{23}{30}=x^{2}+1.33333209-0.2503098580596087565x_{1}$$

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

$$x^{2}+1.33333209-0.2503098580596087565x_{1}=\frac{23}{30}$$

Subtract x^{2} from both sides.

$$1.33333209-0.2503098580596087565x_{1}=\frac{23}{30}-x^{2}$$

Subtract 1.33333209 from both sides.

$$-0.2503098580596087565x_{1}=\frac{23}{30}-x^{2}-1.33333209$$

Subtract 1.33333209 from \frac{23}{30} to get -\frac{169999627}{300000000}.

$$-0.2503098580596087565x_{1}=-\frac{169999627}{300000000}-x^{2}$$

The equation is in standard form.

$$-0.2503098580596087565x_{1}=-x^{2}-\frac{169999627}{300000000}$$

Divide both sides of the equation by -0.2503098580596087565, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-0.2503098580596087565x_{1}}{-0.2503098580596087565}=\frac{-x^{2}-\frac{169999627}{300000000}}{-0.2503098580596087565}$$

Dividing by -0.2503098580596087565 undoes the multiplication by -0.2503098580596087565.

$$x_{1}=\frac{-x^{2}-\frac{169999627}{300000000}}{-0.2503098580596087565}$$

Divide -\frac{169999627}{300000000}-x^{2} by -0.2503098580596087565 by multiplying -\frac{169999627}{300000000}-x^{2} by the reciprocal of -0.2503098580596087565.

$$x_{1}=\frac{2000000000000000000x^{2}}{500619716119217513}+\frac{485713220000000000}{214551306908236077}$$

Solve for x

$$x=\frac{\sqrt{1501859148357652539x_{1}-3399992540000000000}}{2}$$

$$x=-\frac{\sqrt{1501859148357652539x_{1}-3399992540000000000}}{2}\text{, }x_{1}\geq \frac{485713220000000000}{214551306908236077}$$