Solve 0.766^2=x^2+1.1547^2-2*1.1547xcos(38)

$${ 0.766 }^{ 2 } = { x }^{ 2 } + { 1.1547 }^{ 2 } -2 \cdot 1.1547x \cos ( 38 )$$

Solve for x_0

$$x_{0}=\frac{2500000000000000000x^{2}+1866440225000000000}{4549580085948409467}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$${(0.766)} ^ {2} = {(x)} ^ {2} + {(1.1547)} ^ {2} - 2 \cdot 1.1547 x 0.788010753606722$$

Calculate 0.766 to the power of 2 and get 0.586756.

$$0.586756=x^{2}+1.1547^{2}-2\times 1.1547x_{0}\times 0.788010753606722$$

Calculate 1.1547 to the power of 2 and get 1.33333209.

$$0.586756=x^{2}+1.33333209-2\times 1.1547x_{0}\times 0.788010753606722$$

Multiply 2 and 1.1547 to get 2.3094.

$$0.586756=x^{2}+1.33333209-2.3094x_{0}\times 0.788010753606722$$

Multiply 2.3094 and 0.788010753606722 to get 1.8198320343793637868.

$$0.586756=x^{2}+1.33333209-1.8198320343793637868x_{0}$$

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

$$x^{2}+1.33333209-1.8198320343793637868x_{0}=0.586756$$

Subtract x^{2} from both sides.

$$1.33333209-1.8198320343793637868x_{0}=0.586756-x^{2}$$

Subtract 1.33333209 from both sides.

$$-1.8198320343793637868x_{0}=0.586756-x^{2}-1.33333209$$

Subtract 1.33333209 from 0.586756 to get -0.74657609.

$$-1.8198320343793637868x_{0}=-0.74657609-x^{2}$$

The equation is in standard form.

$$-1.8198320343793637868x_{0}=-x^{2}-0.74657609$$

Divide both sides of the equation by -1.8198320343793637868, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-1.8198320343793637868x_{0}}{-1.8198320343793637868}=\frac{-x^{2}-0.74657609}{-1.8198320343793637868}$$

Dividing by -1.8198320343793637868 undoes the multiplication by -1.8198320343793637868.

$$x_{0}=\frac{-x^{2}-0.74657609}{-1.8198320343793637868}$$

Divide -0.74657609-x^{2} by -1.8198320343793637868 by multiplying -0.74657609-x^{2} by the reciprocal of -1.8198320343793637868.

$$x_{0}=\frac{2500000000000000000x^{2}+1866440225000000000}{4549580085948409467}$$

Solve for x

$$x=\frac{\sqrt{\frac{4549580085948409467x_{0}}{625000000000000000}-2.98630436}}{2}$$

$$x=-\frac{\sqrt{\frac{4549580085948409467x_{0}}{625000000000000000}-2.98630436}}{2}\text{, }x_{0}\geq \frac{1866440225000000000}{4549580085948409467}$$