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666-x^{2}=0
Multiply x and x to get x^{2}.
-x^{2}=-666
Subtract 666 from both sides. Anything subtracted from zero gives its negation.
x^{2}=\frac{-666}{-1}
Divide both sides by -1.
x^{2}=666
Fraction \frac{-666}{-1} can be simplified to 666 by removing the negative sign from both the numerator and the denominator.
x=3\sqrt{74} x=-3\sqrt{74}
Take the square root of both sides of the equation.
666-x^{2}=0
Multiply x and x to get x^{2}.
-x^{2}+666=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 666}}{2\left(-1\right)}
This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 666 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-1\right)\times 666}}{2\left(-1\right)}
Square 0.
x=\frac{0±\sqrt{4\times 666}}{2\left(-1\right)}
Multiply -4 times -1.
x=\frac{0±\sqrt{2664}}{2\left(-1\right)}
Multiply 4 times 666.
x=\frac{0±6\sqrt{74}}{2\left(-1\right)}
Take the square root of 2664.
x=\frac{0±6\sqrt{74}}{-2}
Multiply 2 times -1.
x=-3\sqrt{74}
Now solve the equation x=\frac{0±6\sqrt{74}}{-2} when ± is plus.
x=3\sqrt{74}
Now solve the equation x=\frac{0±6\sqrt{74}}{-2} when ± is minus.
x=-3\sqrt{74} x=3\sqrt{74}
The equation is now solved.