Linear Algebra Examples

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

Step 1

Add $8$ to both sides of the equation.

$2 x^{2} = 8$

Step 2

Divide each term in $2 x^{2} = 8$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 x^{2} = 8$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{8}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{8}{2}$

Step 2.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{8}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $8$ by $2$ .

$x^{2} = 4$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{4}$

Step 4

Simplify $\pm \sqrt{4}$ .

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Step 4.1

Rewrite $4$ as $2^{2}$ .

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

Step 4.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 2$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 2$

Step 5.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 2$

Step 5.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 2, - 2$

Step 6

The domain is the set of all valid $x$ values.

${x | x = 2, - 2}$

Step 7