How to solve x ^ 2 + 2 = 0

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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Question

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

Solve for x (complex solution)

$x=-\sqrt{2}i\approx -0-1.414213562i$
$x=\sqrt{2}i\approx 1.414213562i$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

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

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

The equation is now solved.

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

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, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

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

Square $0$.

$$x=\frac{0±\sqrt{-4\times 2}}{2}$$

Multiply $-4$ times $2$.

$$x=\frac{0±\sqrt{-8}}{2}$$

Take the square root of $-8$.

$$x=\frac{0±2\sqrt{2}i}{2}$$

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

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

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

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

The equation is now solved.

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

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Example

Question

Solve for x (complex solution)

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula