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-y^{2}=-5
Subtract 5 from both sides. Anything subtracted from zero gives its negation.
y^{2}=\frac{-5}{-1}
Divide both sides by -1.
y^{2}=5
Fraction \frac{-5}{-1} can be simplified to 5 by removing the negative sign from both the numerator and the denominator.
y=\sqrt{5} y=-\sqrt{5}
Take the square root of both sides of the equation.
-y^{2}+5=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.
y=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 5}}{2\left(-1\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
y=\frac{0±\sqrt{-4\left(-1\right)\times 5}}{2\left(-1\right)}
Square 0.
y=\frac{0±\sqrt{4\times 5}}{2\left(-1\right)}
Multiply -4 times -1.
y=\frac{0±\sqrt{20}}{2\left(-1\right)}
Multiply 4 times 5.
y=\frac{0±2\sqrt{5}}{2\left(-1\right)}
Take the square root of 20.
y=\frac{0±2\sqrt{5}}{-2}
Multiply 2 times -1.
y=-\sqrt{5}
Now solve the equation y=\frac{0±2\sqrt{5}}{-2} when ± is plus.
y=\sqrt{5}
Now solve the equation y=\frac{0±2\sqrt{5}}{-2} when ± is minus.
y=-\sqrt{5} y=\sqrt{5}
The equation is now solved.