Solve for a (complex solution)
a=\frac{x^{2}-\sqrt{x+1}-1}{2}
Solve for a
a=\frac{x^{2}-\sqrt{x+1}-1}{2}
x\geq -1
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x^{2}-2a=1+\sqrt{x+1}
Swap sides so that all variable terms are on the left hand side.
-2a=1+\sqrt{x+1}-x^{2}
Subtract x^{2} from both sides.
-2a=-x^{2}+\sqrt{x+1}+1
The equation is in standard form.
\frac{-2a}{-2}=\frac{-x^{2}+\sqrt{x+1}+1}{-2}
Divide both sides by -2.
a=\frac{-x^{2}+\sqrt{x+1}+1}{-2}
Dividing by -2 undoes the multiplication by -2.
a=\frac{x^{2}-\sqrt{x+1}-1}{2}
Divide 1+\sqrt{x+1}-x^{2} by -2.
x^{2}-2a=1+\sqrt{x+1}
Swap sides so that all variable terms are on the left hand side.
-2a=1+\sqrt{x+1}-x^{2}
Subtract x^{2} from both sides.
-2a=-x^{2}+\sqrt{x+1}+1
The equation is in standard form.
\frac{-2a}{-2}=\frac{-x^{2}+\sqrt{x+1}+1}{-2}
Divide both sides by -2.
a=\frac{-x^{2}+\sqrt{x+1}+1}{-2}
Dividing by -2 undoes the multiplication by -2.
a=\frac{x^{2}-\sqrt{x+1}-1}{2}
Divide 1+\sqrt{x+1}-x^{2} by -2.
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