How to solve x ^ 2 - 8 = 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 x ^ 2 - 8 = 0 | Equatix

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Question

$$x^{2}-8=0$$

Solve for x

$x=2\sqrt{2}\approx 2.828427125$
$x=-2\sqrt{2}\approx -2.828427125$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Add $8$ to both sides. Anything plus zero gives itself.

$$x^{2}=8$$

Take the square root of both sides of the equation.

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

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

$$x^{2}-8=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-8$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-8\right)}}{2}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-8\right)}}{2}$$

Multiply $-4$ times $-8$.

$$x=\frac{0±\sqrt{32}}{2}$$

Take the square root of $32$.

$$x=\frac{0±4\sqrt{2}}{2}$$

Now solve the equation $x=\frac{0±4\sqrt{2}}{2}$ when $±$ is plus.

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

Now solve the equation $x=\frac{0±4\sqrt{2}}{2}$ when $±$ is minus.

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

The equation is now solved.

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

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

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