Solve 49=81+x^2-2*9xcos(28.647889)

$$49 = 81+ { x }^{ 2 } -2 \cdot 9x \cos ( 28.647889 )$$

Solve for x_0

$$x_{0}=\frac{5000000000000000x^{2}+160000000000000000}{78982431139869471}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$49 = 81 + {(x)} ^ {2} - 2 \cdot 9 x 0.8775825682207719$$

Multiply 2 and 9 to get 18.

$$49=81+x^{2}-18x_{0}\times 0.8775825682207719$$

Multiply 18 and 0.8775825682207719 to get 15.7964862279738942.

$$49=81+x^{2}-15.7964862279738942x_{0}$$

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

$$81+x^{2}-15.7964862279738942x_{0}=49$$

Subtract 81 from both sides.

$$x^{2}-15.7964862279738942x_{0}=49-81$$

Subtract 81 from 49 to get -32.

$$x^{2}-15.7964862279738942x_{0}=-32$$

Subtract x^{2} from both sides.

$$-15.7964862279738942x_{0}=-32-x^{2}$$

The equation is in standard form.

$$-15.7964862279738942x_{0}=-x^{2}-32$$

Divide both sides of the equation by -15.7964862279738942, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-15.7964862279738942x_{0}}{-15.7964862279738942}=\frac{-x^{2}-32}{-15.7964862279738942}$$

Dividing by -15.7964862279738942 undoes the multiplication by -15.7964862279738942.

$$x_{0}=\frac{-x^{2}-32}{-15.7964862279738942}$$

Divide -32-x^{2} by -15.7964862279738942 by multiplying -32-x^{2} by the reciprocal of -15.7964862279738942.

$$x_{0}=\frac{5000000000000000x^{2}+160000000000000000}{78982431139869471}$$

Solve for x (complex solution)

$$x=-\sqrt{\frac{78982431139869471x_{0}}{5000000000000000}-32}$$

$$x=\sqrt{\frac{78982431139869471x_{0}}{5000000000000000}-32}$$

Solve for x

$$x=\frac{\sqrt{\frac{78982431139869471x_{0}}{1250000000000000}-128}}{2}$$

$$x=-\frac{\sqrt{\frac{78982431139869471x_{0}}{1250000000000000}-128}}{2}\text{, }x_{0}\geq \frac{160000000000000000}{78982431139869471}$$