Solve for x
Solve for y
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x^{2}-1=y
Swap sides so that all variable terms are on the left hand side.
x^{2}=y+1
x=\sqrt{y+1} x=-\sqrt{y+1}
Take the square root of both sides of the equation.
x^{2}-1=y
Swap sides so that all variable terms are on the left hand side.
x^{2}-1-y=0
Subtract y from both sides.
x^{2}-y-1=0
Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.
x=\frac{0±\sqrt{0^{2}-4\left(-y-1\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1-y for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-y-1\right)}}{2}
Square 0.
x=\frac{0±\sqrt{4y+4}}{2}
Multiply -4 times -1-y.
x=\frac{0±2\sqrt{y+1}}{2}
Take the square root of 4+4y.
x=\sqrt{y+1}
Now solve the equation x=\frac{0±2\sqrt{y+1}}{2} when ± is plus.
x=-\sqrt{y+1}
Now solve the equation x=\frac{0±2\sqrt{y+1}}{2} when ± is minus.
x=\sqrt{y+1} x=-\sqrt{y+1}
The equation is now solved.