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-x^{2}=-25
Subtract 25 from both sides. Anything subtracted from zero gives its negation.
x^{2}=\frac{-25}{-1}
Divide both sides by -1.
x^{2}=25
Fraction \frac{-25}{-1} can be simplified to 25 by removing the negative sign from both the numerator and the denominator.
x=5 x=-5
Take the square root of both sides of the equation.
-x^{2}+25=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(-1\right)\times 25}}{2\left(-1\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-1\right)\times 25}}{2\left(-1\right)}
Square 0.
x=\frac{0±\sqrt{4\times 25}}{2\left(-1\right)}
Multiply -4 times -1.
x=\frac{0±\sqrt{100}}{2\left(-1\right)}
Multiply 4 times 25.
x=\frac{0±10}{2\left(-1\right)}
Take the square root of 100.
x=\frac{0±10}{-2}
Multiply 2 times -1.
x=-5
Now solve the equation x=\frac{0±10}{-2} when ± is plus. Divide 10 by -2.
x=5
Now solve the equation x=\frac{0±10}{-2} when ± is minus. Divide -10 by -2.
x=-5 x=5
The equation is now solved.