Solve 2cos4=a^2

$$2 \cos 4 = a ^ { 2 }$$

Solve for a

$$a = \frac{\sqrt{4987820251299121}}{50000000} \approx 1.412490036$$

$$a = -\frac{\sqrt{4987820251299121}}{50000000} \approx -1.412490036$$

Steps by Finding Square Root

Evaluate trigonometric functions in the problem

$$2 \cdot 0.9975640502598242 = a ^ {2}$$

Multiply 2 and 0.9975640502598242 to get 1.9951281005196484.

$$1.9951281005196484=a^{2}$$

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

$$a^{2}=1.9951281005196484$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{4987820251299121}}{50000000} a=-\frac{\sqrt{4987820251299121}}{50000000}$$

Steps Using the Quadratic Formula

Evaluate trigonometric functions in the problem

$$2 \cdot 0.9975640502598242 = a ^ {2}$$

Multiply 2 and 0.9975640502598242 to get 1.9951281005196484.

$$1.9951281005196484=a^{2}$$

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

$$a^{2}=1.9951281005196484$$

Subtract 1.9951281005196484 from both sides.

$$a^{2}-1.9951281005196484=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1.9951281005196484 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-1.9951281005196484\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-1.9951281005196484\right)}}{2}$$

Multiply -4 times -1.9951281005196484.

$$a=\frac{0±\sqrt{7.9805124020785936}}{2}$$

Take the square root of 7.9805124020785936.

$$a=\frac{0±\frac{\sqrt{4987820251299121}}{25000000}}{2}$$

Now solve the equation a=\frac{0±\frac{\sqrt{4987820251299121}}{25000000}}{2} when ± is plus.

$$a=\frac{\sqrt{4987820251299121}}{50000000}$$

Now solve the equation a=\frac{0±\frac{\sqrt{4987820251299121}}{25000000}}{2} when ± is minus.

$$a=-\frac{\sqrt{4987820251299121}}{50000000}$$

The equation is now solved.

$$a=\frac{\sqrt{4987820251299121}}{50000000} a=-\frac{\sqrt{4987820251299121}}{50000000}$$