Solve -1x^2+2=0

$$- 1 x ^ { 2 } + 2 = 0$$

Solve for x

$$x=\sqrt{2}\approx 1.414213562$$

$$x=-\sqrt{2}\approx -1.414213562$$

Steps by Finding Square Root

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

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

Divide both sides by -1.

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

Fraction \frac{-2}{-1} can be simplified to 2 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=2$$

Take the square root of both sides of the equation.

$$x=\sqrt{2} x=-\sqrt{2}$$

Steps Using the Quadratic Formula

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.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -1.

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

Multiply 4 times 2.

$$x=\frac{0±\sqrt{8}}{2\left(-1\right)}$$

Take the square root of 8.

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

Multiply 2 times -1.

$$x=\frac{0±2\sqrt{2}}{-2}$$

Now solve the equation x=\frac{0±2\sqrt{2}}{-2} when ± is plus.

$$x=-\sqrt{2}$$

Now solve the equation x=\frac{0±2\sqrt{2}}{-2} when ± is minus.

$$x=\sqrt{2}$$

The equation is now solved.

$$x=-\sqrt{2} x=\sqrt{2}$$