Solve 2x+3sqrt{2/2}=4y*sin(25^2)

$$2x+3 \sqrt{ \frac{ 2 }{ 2 } } =4y \times \sin ( { 25 }^{ 2 } )$$

Solve for x

$$x=-\frac{1992389396183491y}{1000000000000000}-1.5$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$2 x + 3 \sqrt{\frac{2}{2}} = 4 y \cdot -0.9961946980917455$$

Divide 2 by 2 to get 1.

$$2x+3\sqrt{1}=4y\left(-0.9961946980917455\right)$$

Calculate the square root of 1 and get 1.

$$2x+3\times 1=4y\left(-0.9961946980917455\right)$$

Multiply 3 and 1 to get 3.

$$2x+3=4y\left(-0.9961946980917455\right)$$

Multiply 4 and -0.9961946980917455 to get -3.984778792366982.

$$2x+3=-3.984778792366982y$$

Subtract 3 from both sides.

$$2x=-3.984778792366982y-3$$

The equation is in standard form.

$$2x=-\frac{1992389396183491y}{500000000000000}-3$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{-\frac{1992389396183491y}{500000000000000}-3}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{-\frac{1992389396183491y}{500000000000000}-3}{2}$$

Divide -\frac{1992389396183491y}{500000000000000}-3 by 2.

$$x=-\frac{1992389396183491y}{1000000000000000}-\frac{3}{2}$$

Solve for y

$$y=\frac{-1000000000000000x-1500000000000000}{1992389396183491}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$2 x + 3 \sqrt{\frac{2}{2}} = 4 y \cdot -0.9961946980917455$$

Divide 2 by 2 to get 1.

$$2x+3\sqrt{1}=4y\left(-0.9961946980917455\right)$$

Calculate the square root of 1 and get 1.

$$2x+3\times 1=4y\left(-0.9961946980917455\right)$$

Multiply 3 and 1 to get 3.

$$2x+3=4y\left(-0.9961946980917455\right)$$

Multiply 4 and -0.9961946980917455 to get -3.984778792366982.

$$2x+3=-3.984778792366982y$$

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

$$-3.984778792366982y=2x+3$$

Divide both sides of the equation by -3.984778792366982, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-3.984778792366982y}{-3.984778792366982}=\frac{2x+3}{-3.984778792366982}$$

Dividing by -3.984778792366982 undoes the multiplication by -3.984778792366982.

$$y=\frac{2x+3}{-3.984778792366982}$$

Divide 2x+3 by -3.984778792366982 by multiplying 2x+3 by the reciprocal of -3.984778792366982.

$$y=\frac{-1000000000000000x-1500000000000000}{1992389396183491}$$