How to solve - x ^ 2 = - 5

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 - x ^ 2 = - 5 | Equatix

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Question

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

Solve for x

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

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Divide both sides by $-1$.

$$x^{2}=\frac{-5}{-1}$$

Fraction $\frac{-5}{-1}$ can be simplified to $5$ by removing the negative sign from both the numerator and the denominator.

$$x^{2}=5$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Add $5$ to both sides.

$$-x^{2}+5=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $-1$ for $a$, $0$ for $b$, and $5$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

Multiply $-4$ times $-1$.

$$x=\frac{0±\sqrt{4\times 5}}{2\left(-1\right)}$$

Multiply $4$ times $5$.

$$x=\frac{0±\sqrt{20}}{2\left(-1\right)}$$

Take the square root of $20$.

$$x=\frac{0±2\sqrt{5}}{2\left(-1\right)}$$

Multiply $2$ times $-1$.

$$x=\frac{0±2\sqrt{5}}{-2}$$

Now solve the equation $x=\frac{0±2\sqrt{5}}{-2}$ when $±$ is plus.

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

Now solve the equation $x=\frac{0±2\sqrt{5}}{-2}$ when $±$ is minus.

$$x=\sqrt{5}$$

The equation is now solved.

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

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

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Example

Question

Solve for x

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula