Solve frac{7x^2+sqrt{pi}}{cossqrt{2}}=y

$$\frac { 7 x ^ { 2 } + \sqrt { \pi } } { \cos \sqrt { 2 } } = y$$

Solve for y

$$y=\frac{5000000000000000\left(7x^{2}+\sqrt{\pi }\right)}{4998476990225973}$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{7 x ^ {2} + \sqrt{\pi}}{0.9996953980451946} = y$$

Divide each term of 7x^{2}+\sqrt{\pi } by 0.9996953980451946 to get \frac{7x^{2}}{0.9996953980451946}+\frac{\sqrt{\pi }}{0.9996953980451946}.

$$\frac{7x^{2}}{0.9996953980451946}+\frac{\sqrt{\pi }}{0.9996953980451946}=y$$

Divide 7x^{2} by 0.9996953980451946 to get \frac{35000000000000000}{4998476990225973}x^{2}.

$$\frac{35000000000000000}{4998476990225973}x^{2}+\frac{\sqrt{\pi }}{0.9996953980451946}=y$$

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

$$y=\frac{35000000000000000}{4998476990225973}x^{2}+\frac{\sqrt{\pi }}{0.9996953980451946}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{69978677863163622y-70000000000000000\sqrt{\pi }}}{700000000}$$

$$x=\frac{\sqrt{69978677863163622y-70000000000000000\sqrt{\pi }}}{700000000}$$

Solve for x

$$x=\frac{\sqrt{69978677863163622y-70000000000000000\sqrt{\pi }}}{700000000}$$

$$x=-\frac{\sqrt{69978677863163622y-70000000000000000\sqrt{\pi }}}{700000000}\text{, }y\geq \frac{5000000000000000\sqrt{\pi }}{4998476990225973}$$