Solve for y (complex solution)
y=25\left(x+2\right)^{-\frac{1}{2}}
x\neq -2
Solve for x
x=-2+\frac{625}{y^{2}}
y>0
Solve for y
y=\frac{25}{\sqrt{x+2}}
x>-2
Solve for x (complex solution)
x=-2+\frac{625}{y^{2}}
arg(\sqrt{\frac{1}{y^{2}}}y)<\pi \text{ and }y\neq 0
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\sqrt{x+2}y=25
The equation is in standard form.
\frac{\sqrt{x+2}y}{\sqrt{x+2}}=\frac{25}{\sqrt{x+2}}
Divide both sides by \sqrt{x+2}.
y=\frac{25}{\sqrt{x+2}}
Dividing by \sqrt{x+2} undoes the multiplication by \sqrt{x+2}.
y=25\left(x+2\right)^{-\frac{1}{2}}
Divide 25 by \sqrt{x+2}.
\frac{y\sqrt{x+2}}{y}=\frac{25}{y}
Divide both sides by y.
\sqrt{x+2}=\frac{25}{y}
Dividing by y undoes the multiplication by y.
x+2=\frac{625}{y^{2}}
Square both sides of the equation.
x+2-2=\frac{625}{y^{2}}-2
Subtract 2 from both sides of the equation.
x=\frac{625}{y^{2}}-2
Subtracting 2 from itself leaves 0.
x=-2+\frac{625}{y^{2}}
Subtract 2 from \frac{625}{y^{2}}.
\sqrt{x+2}y=25
The equation is in standard form.
\frac{\sqrt{x+2}y}{\sqrt{x+2}}=\frac{25}{\sqrt{x+2}}
Divide both sides by \sqrt{x+2}.
y=\frac{25}{\sqrt{x+2}}
Dividing by \sqrt{x+2} undoes the multiplication by \sqrt{x+2}.
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