Solve 2*320*cos37^circ=1/2*50*x^2

$$2 \times 320 \times \cos 37 ^ { \circ } = \frac { 1 } { 2 } \times 50 \times x ^ { 2 }$$

Solve for x

$$x = \frac{\sqrt{1247867984448895}}{7812500} \approx 4.521622392$$

$$x = -\frac{\sqrt{1247867984448895}}{7812500} \approx -4.521622392$$

Steps by Finding Square Root

Evaluate trigonometric functions in the problem

$$2 \cdot 320 \cdot 0.7986355100472928 = \frac{1}{2} \cdot 50 \cdot x ^ {2}$$

Multiply 2 and 320 to get 640.

$$640\times 0.7986355100472928=\frac{1}{2}\times 50x^{2}$$

Multiply 640 and 0.7986355100472928 to get 511.126726430267392.

$$511.126726430267392=\frac{1}{2}\times 50x^{2}$$

Multiply \frac{1}{2} and 50 to get 25.

$$511.126726430267392=25x^{2}$$

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

$$25x^{2}=511.126726430267392$$

Divide both sides by 25.

$$x^{2}=\frac{511.126726430267392}{25}$$

Expand \frac{511.126726430267392}{25} by multiplying both numerator and the denominator by 1000000000000000.

$$x^{2}=\frac{511126726430267392}{25000000000000000}$$

Reduce the fraction \frac{511126726430267392}{25000000000000000} to lowest terms by extracting and canceling out 2048.

$$x^{2}=\frac{249573596889779}{12207031250000}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{1247867984448895}}{7812500} x=-\frac{\sqrt{1247867984448895}}{7812500}$$

Steps Using the Quadratic Formula

Evaluate trigonometric functions in the problem

$$2 \cdot 320 \cdot 0.7986355100472928 = \frac{1}{2} \cdot 50 \cdot x ^ {2}$$

Multiply 2 and 320 to get 640.

$$640\times 0.7986355100472928=\frac{1}{2}\times 50x^{2}$$

Multiply 640 and 0.7986355100472928 to get 511.126726430267392.

$$511.126726430267392=\frac{1}{2}\times 50x^{2}$$

Multiply \frac{1}{2} and 50 to get 25.

$$511.126726430267392=25x^{2}$$

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

$$25x^{2}=511.126726430267392$$

Subtract 511.126726430267392 from both sides.

$$25x^{2}-511.126726430267392=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 0 for b, and -511.126726430267392 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 25\left(-511.126726430267392\right)}}{2\times 25}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 25\left(-511.126726430267392\right)}}{2\times 25}$$

Multiply -4 times 25.

$$x=\frac{0±\sqrt{-100\left(-511.126726430267392\right)}}{2\times 25}$$

Multiply -100 times -511.126726430267392.

$$x=\frac{0±\sqrt{51112.6726430267392}}{2\times 25}$$

Take the square root of 51112.6726430267392.

$$x=\frac{0±\frac{\sqrt{1247867984448895}}{156250}}{2\times 25}$$

Multiply 2 times 25.

$$x=\frac{0±\frac{\sqrt{1247867984448895}}{156250}}{50}$$

Now solve the equation x=\frac{0±\frac{\sqrt{1247867984448895}}{156250}}{50} when ± is plus.

$$x=\frac{\sqrt{1247867984448895}}{7812500}$$

Now solve the equation x=\frac{0±\frac{\sqrt{1247867984448895}}{156250}}{50} when ± is minus.

$$x=-\frac{\sqrt{1247867984448895}}{7812500}$$

The equation is now solved.

$$x=\frac{\sqrt{1247867984448895}}{7812500} x=-\frac{\sqrt{1247867984448895}}{7812500}$$