Solve x^2+sqrt{2}=-sqrt{2}

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

Solve for x (complex solution)

$$x=-2^{\frac{3}{4}}i\approx -0-1.681792831i$$

$$x=2^{\frac{3}{4}}i\approx 1.681792831i$$

Steps by Finding Square Root

Subtract \sqrt{2} from both sides.

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

Combine -\sqrt{2} and -\sqrt{2} to get -2\sqrt{2}.

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

The equation is now solved.

$$x=2^{\frac{3}{4}}i x=-2^{\frac{3}{4}}i$$

Steps Using the Quadratic Formula

Add \sqrt{2} to both sides.

$$x^{2}+\sqrt{2}+\sqrt{2}=0$$

Combine \sqrt{2} and \sqrt{2} to get 2\sqrt{2}.

$$x^{2}+2\sqrt{2}=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\times 2\sqrt{2}}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\sqrt{2}}}{2}$$

Multiply -4 times 2\sqrt{2}.

$$x=\frac{0±\sqrt{-8\sqrt{2}}}{2}$$

Take the square root of -8\sqrt{2}.

$$x=\frac{0±2\times 2^{\frac{3}{4}}i}{2}$$

Now solve the equation x=\frac{0±2\times 2^{\frac{3}{4}}i}{2} when ± is plus.

$$x=2^{\frac{3}{4}}i$$

Now solve the equation x=\frac{0±2\times 2^{\frac{3}{4}}i}{2} when ± is minus.

$$x=-2^{\frac{3}{4}}i$$

The equation is now solved.

$$x=2^{\frac{3}{4}}i x=-2^{\frac{3}{4}}i$$