Solve for n (complex solution)
n=-\left(12-x\right)^{-\frac{1}{2}}\left(\sqrt{x+14}-2\right)
x\neq 12
Solve for n
n=-\frac{\sqrt{x+14}-2}{\sqrt{12-x}}
x\geq -14\text{ and }x<12
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n\sqrt{12-x}=2-\sqrt{14+x}
Subtract \sqrt{14+x} from both sides.
\sqrt{12-x}n=-\sqrt{x+14}+2
The equation is in standard form.
\frac{\sqrt{12-x}n}{\sqrt{12-x}}=\frac{-\sqrt{x+14}+2}{\sqrt{12-x}}
Divide both sides by \sqrt{12-x}.
n=\frac{-\sqrt{x+14}+2}{\sqrt{12-x}}
Dividing by \sqrt{12-x} undoes the multiplication by \sqrt{12-x}.
n=\left(12-x\right)^{-\frac{1}{2}}\left(-\sqrt{x+14}+2\right)
Divide 2-\sqrt{14+x} by \sqrt{12-x}.
n\sqrt{12-x}=2-\sqrt{14+x}
Subtract \sqrt{14+x} from both sides.
\sqrt{12-x}n=-\sqrt{x+14}+2
The equation is in standard form.
\frac{\sqrt{12-x}n}{\sqrt{12-x}}=\frac{-\sqrt{x+14}+2}{\sqrt{12-x}}
Divide both sides by \sqrt{12-x}.
n=\frac{-\sqrt{x+14}+2}{\sqrt{12-x}}
Dividing by \sqrt{12-x} undoes the multiplication by \sqrt{12-x}.
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