How to solve 2(x)^(2)+10=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.

Solve 2(x)^(2)+10=0 | Equatix

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Question

$$2 { x }^{ 2 } +10=0$$

Solve for x (complex solution)

$x=-\sqrt{5}i\approx -0-2.236067977i$
$x=\sqrt{5}i\approx 2.236067977i$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Subtract $10$ from both sides. Anything subtracted from zero gives its negation.

$$2x^{2}=-10$$

Divide both sides by $2$.

$$x^{2}=\frac{-10}{2}$$

Divide $-10$ by $2$ to get $-5$.

$$x^{2}=-5$$

The equation is now solved.

$$x=\sqrt{5}i$$ $$x=-\sqrt{5}i$$

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: $ax^{2}+bx+c=0$.

$$2x^{2}+10=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $2$ for $a$, $0$ for $b$, and $10$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 10}}{2\times 2}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 2\times 10}}{2\times 2}$$

Multiply $-4$ times $2$.

$$x=\frac{0±\sqrt{-8\times 10}}{2\times 2}$$

Multiply $-8$ times $10$.

$$x=\frac{0±\sqrt{-80}}{2\times 2}$$

Take the square root of $-80$.

$$x=\frac{0±4\sqrt{5}i}{2\times 2}$$

Multiply $2$ times $2$.

$$x=\frac{0±4\sqrt{5}i}{4}$$

Now solve the equation $x=\frac{0±4\sqrt{5}i}{4}$ when $±$ is plus.

$$x=\sqrt{5}i$$

Now solve the equation $x=\frac{0±4\sqrt{5}i}{4}$ when $±$ is minus.

$$x=-\sqrt{5}i$$

The equation is now solved.

$$x=\sqrt{5}i$$ $$x=-\sqrt{5}i$$

Show Solution

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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