Solve x^2=(20)^2+(20)^2-2(20)(20)cos140

$$x ^ { 2 } = ( 20 ) ^ { 2 } + ( 20 ) ^ { 2 } - 2 ( 20 ) ( 20 ) \cos 140$$

Solve for x

$$x = \frac{3 \sqrt{3924543206931062}}{5000000} \approx 37.587704831$$

$$x = -\frac{3 \sqrt{3924543206931062}}{5000000} \approx -37.587704831$$

Steps by Finding Square Root

Evaluate trigonometric functions in the problem

$$x ^ {2} = {(20)} ^ {2} + {(20)} ^ {2} - 2 {(20)} {(20)} \cdot -0.7660444431189779$$

Calculate 20 to the power of 2 and get 400.

$$x^{2}=400+20^{2}-2\times 20\times 20\left(-0.7660444431189779\right)$$

Calculate 20 to the power of 2 and get 400.

$$x^{2}=400+400-2\times 20\times 20\left(-0.7660444431189779\right)$$

Add 400 and 400 to get 800.

$$x^{2}=800-2\times 20\times 20\left(-0.7660444431189779\right)$$

Multiply 2 and 20 to get 40.

$$x^{2}=800-40\times 20\left(-0.7660444431189779\right)$$

Multiply 40 and 20 to get 800.

$$x^{2}=800-800\left(-0.7660444431189779\right)$$

Multiply 800 and -0.7660444431189779 to get -612.83555449518232.

$$x^{2}=800-\left(-612.83555449518232\right)$$

The opposite of -612.83555449518232 is 612.83555449518232.

$$x^{2}=800+612.83555449518232$$

Add 800 and 612.83555449518232 to get 1412.83555449518232.

$$x^{2}=1412.83555449518232$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{3924543206931062}}{5000000} x=-\frac{3\sqrt{3924543206931062}}{5000000}$$

Steps Using the Quadratic Formula

Evaluate trigonometric functions in the problem

$$x ^ {2} = {(20)} ^ {2} + {(20)} ^ {2} - 2 {(20)} {(20)} \cdot -0.7660444431189779$$

Calculate 20 to the power of 2 and get 400.

$$x^{2}=400+20^{2}-2\times 20\times 20\left(-0.7660444431189779\right)$$

Calculate 20 to the power of 2 and get 400.

$$x^{2}=400+400-2\times 20\times 20\left(-0.7660444431189779\right)$$

Add 400 and 400 to get 800.

$$x^{2}=800-2\times 20\times 20\left(-0.7660444431189779\right)$$

Multiply 2 and 20 to get 40.

$$x^{2}=800-40\times 20\left(-0.7660444431189779\right)$$

Multiply 40 and 20 to get 800.

$$x^{2}=800-800\left(-0.7660444431189779\right)$$

Multiply 800 and -0.7660444431189779 to get -612.83555449518232.

$$x^{2}=800-\left(-612.83555449518232\right)$$

The opposite of -612.83555449518232 is 612.83555449518232.

$$x^{2}=800+612.83555449518232$$

Add 800 and 612.83555449518232 to get 1412.83555449518232.

$$x^{2}=1412.83555449518232$$

Subtract 1412.83555449518232 from both sides.

$$x^{2}-1412.83555449518232=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1412.83555449518232 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1412.83555449518232\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1412.83555449518232\right)}}{2}$$

Multiply -4 times -1412.83555449518232.

$$x=\frac{0±\sqrt{5651.34221798072928}}{2}$$

Take the square root of 5651.34221798072928.

$$x=\frac{0±\frac{3\sqrt{3924543206931062}}{2500000}}{2}$$

Now solve the equation x=\frac{0±\frac{3\sqrt{3924543206931062}}{2500000}}{2} when ± is plus.

$$x=\frac{3\sqrt{3924543206931062}}{5000000}$$

Now solve the equation x=\frac{0±\frac{3\sqrt{3924543206931062}}{2500000}}{2} when ± is minus.

$$x=-\frac{3\sqrt{3924543206931062}}{5000000}$$

The equation is now solved.

$$x=\frac{3\sqrt{3924543206931062}}{5000000} x=-\frac{3\sqrt{3924543206931062}}{5000000}$$