Solve 4*10^-5*X^2cos53^circ=6*10^-6

$$4 \times 10 ^ { - 5 } \times X ^ { 2 } \cos 53 ^ { \circ } = 6 \times 10 ^ { - 6 }$$

Solve for X

$$X=\frac{5000000\sqrt{22568063368201815}}{1504537557880121}\approx 0.499245452$$

$$X=-\frac{5000000\sqrt{22568063368201815}}{1504537557880121}\approx -0.499245452$$

Steps by Finding Square Root

Evaluate trigonometric functions in the problem

$$4 \cdot 10 ^ {-5} \cdot X ^ {2} 0.6018150231520484 = 6 \cdot 10 ^ {-6}$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$4\times \frac{1}{100000}X^{2}\times 0.6018150231520484=6\times 10^{-6}$$

Multiply 4 and \frac{1}{100000} to get \frac{1}{25000}.

$$\frac{1}{25000}X^{2}\times 0.6018150231520484=6\times 10^{-6}$$

Multiply \frac{1}{25000} and 0.6018150231520484 to get \frac{1504537557880121}{62500000000000000000}.

$$\frac{1504537557880121}{62500000000000000000}X^{2}=6\times 10^{-6}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{1504537557880121}{62500000000000000000}X^{2}=6\times \frac{1}{1000000}$$

Multiply 6 and \frac{1}{1000000} to get \frac{3}{500000}.

$$\frac{1504537557880121}{62500000000000000000}X^{2}=\frac{3}{500000}$$

Multiply both sides by \frac{62500000000000000000}{1504537557880121}, the reciprocal of \frac{1504537557880121}{62500000000000000000}.

$$X^{2}=\frac{3}{500000}\times \frac{62500000000000000000}{1504537557880121}$$

Multiply \frac{3}{500000} and \frac{62500000000000000000}{1504537557880121} to get \frac{375000000000000}{1504537557880121}.

$$X^{2}=\frac{375000000000000}{1504537557880121}$$

Take the square root of both sides of the equation.

$$X=\frac{5000000\sqrt{22568063368201815}}{1504537557880121} X=-\frac{5000000\sqrt{22568063368201815}}{1504537557880121}$$

Steps Using the Quadratic Formula

Evaluate trigonometric functions in the problem

$$4 \cdot 10 ^ {-5} \cdot X ^ {2} 0.6018150231520484 = 6 \cdot 10 ^ {-6}$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$4\times \frac{1}{100000}X^{2}\times 0.6018150231520484=6\times 10^{-6}$$

Multiply 4 and \frac{1}{100000} to get \frac{1}{25000}.

$$\frac{1}{25000}X^{2}\times 0.6018150231520484=6\times 10^{-6}$$

Multiply \frac{1}{25000} and 0.6018150231520484 to get \frac{1504537557880121}{62500000000000000000}.

$$\frac{1504537557880121}{62500000000000000000}X^{2}=6\times 10^{-6}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{1504537557880121}{62500000000000000000}X^{2}=6\times \frac{1}{1000000}$$

Multiply 6 and \frac{1}{1000000} to get \frac{3}{500000}.

$$\frac{1504537557880121}{62500000000000000000}X^{2}=\frac{3}{500000}$$

Subtract \frac{3}{500000} from both sides.

$$\frac{1504537557880121}{62500000000000000000}X^{2}-\frac{3}{500000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1504537557880121}{62500000000000000000} for a, 0 for b, and -\frac{3}{500000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$X=\frac{0±\sqrt{0^{2}-4\times \frac{1504537557880121}{62500000000000000000}\left(-\frac{3}{500000}\right)}}{2\times \frac{1504537557880121}{62500000000000000000}}$$

Square 0.

$$X=\frac{0±\sqrt{-4\times \frac{1504537557880121}{62500000000000000000}\left(-\frac{3}{500000}\right)}}{2\times \frac{1504537557880121}{62500000000000000000}}$$

Multiply -4 times \frac{1504537557880121}{62500000000000000000}.

$$X=\frac{0±\sqrt{-\frac{1504537557880121}{15625000000000000000}\left(-\frac{3}{500000}\right)}}{2\times \frac{1504537557880121}{62500000000000000000}}$$

Multiply -\frac{1504537557880121}{15625000000000000000} times -\frac{3}{500000} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$X=\frac{0±\sqrt{\frac{4513612673640363}{7812500000000000000000000}}}{2\times \frac{1504537557880121}{62500000000000000000}}$$

Take the square root of \frac{4513612673640363}{7812500000000000000000000}.

$$X=\frac{0±\frac{\sqrt{22568063368201815}}{6250000000000}}{2\times \frac{1504537557880121}{62500000000000000000}}$$

Multiply 2 times \frac{1504537557880121}{62500000000000000000}.

$$X=\frac{0±\frac{\sqrt{22568063368201815}}{6250000000000}}{\frac{1504537557880121}{31250000000000000000}}$$

Now solve the equation X=\frac{0±\frac{\sqrt{22568063368201815}}{6250000000000}}{\frac{1504537557880121}{31250000000000000000}} when ± is plus.

$$X=\frac{5000000\sqrt{22568063368201815}}{1504537557880121}$$

Now solve the equation X=\frac{0±\frac{\sqrt{22568063368201815}}{6250000000000}}{\frac{1504537557880121}{31250000000000000000}} when ± is minus.

$$X=-\frac{5000000\sqrt{22568063368201815}}{1504537557880121}$$

The equation is now solved.

$$X=\frac{5000000\sqrt{22568063368201815}}{1504537557880121} X=-\frac{5000000\sqrt{22568063368201815}}{1504537557880121}$$