Solve 666-xx=0

$$666-xx=0$$

Solve for x

$$x=3\sqrt{74}\approx 25.806975801$$

$$x=-3\sqrt{74}\approx -25.806975801$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$666-x^{2}=0$$

Subtract 666 from both sides. Anything subtracted from zero gives its negation.

$$-x^{2}=-666$$

Divide both sides by -1.

$$x^{2}=\frac{-666}{-1}$$

Fraction \frac{-666}{-1} can be simplified to 666 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=666$$

Take the square root of both sides of the equation.

$$x=3\sqrt{74} x=-3\sqrt{74}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$666-x^{2}=0$$

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.

$$-x^{2}+666=0$$

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}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 666}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 666}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 666}}{2\left(-1\right)}$$

Multiply 4 times 666.

$$x=\frac{0±\sqrt{2664}}{2\left(-1\right)}$$

Take the square root of 2664.

$$x=\frac{0±6\sqrt{74}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±6\sqrt{74}}{-2}$$

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.

$$x=3\sqrt{74}$$

The equation is now solved.

$$x=-3\sqrt{74} x=3\sqrt{74}$$