Solve 25^y=100*sqrt{x}+1/y=

$$25 ^ { y } = 100 \cdot \sqrt { x } + \frac { 1 } { y } =$$

Solve for x

$$x=\frac{\left(-25^{y}+\frac{1}{y}\right)^{2}}{10000}$$

$$\left(\frac{|1-y\times 25^{y}|}{|y|}\leq 0\text{ or }-\frac{25^{y}}{100}+\frac{1}{100y}\leq 0\right)\text{ and }y\neq 0$$

Steps for Solving Radical Equations

Multiply both sides of the equation by y.

$$y\times 25^{y}=100\sqrt{x}y+1$$

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

$$100\sqrt{x}y+1=y\times 25^{y}$$

Subtract 1 from both sides.

$$100\sqrt{x}y=y\times 25^{y}-1$$

Divide both sides by 100y.

$$\frac{100y\sqrt{x}}{100y}=\frac{y\times 25^{y}-1}{100y}$$

Dividing by 100y undoes the multiplication by 100y.

$$\sqrt{x}=\frac{y\times 25^{y}-1}{100y}$$

Square both sides of the equation.

$$x=\frac{\left(y\times 25^{y}-1\right)^{2}}{10000y^{2}}$$

Solve for x (complex solution)

$$x=\frac{\left(-25^{y}+\frac{1}{y}\right)^{2}}{10000}$$

$$\left(y\neq 0\text{ and }1-y\times 25^{y}=0\text{ and }\frac{1-y\times 25^{y}}{100}=0\right)\text{ or }\left(y\neq 0\text{ and }arg(-\frac{25^{y}}{100}+\frac{1}{100y})\geq \pi \text{ and }\frac{1-y\times 25^{y}}{100}\neq 0\right)$$