Algebra Examples

$\frac{1}{2} x^{2} = 6$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} x^{2}) = 2 \cdot 6$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $2 (\frac{1}{2} x^{2})$ .

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Step 2.1.1.1

Combine $\frac{1}{2}$ and $x^{2}$ .

$2 \frac{x^{2}}{2} = 2 \cdot 6$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Cancel the common factor.

$2 \frac{x^{2}}{2} = 2 \cdot 6$

Step 2.1.1.2.2

Rewrite the expression.

$x^{2} = 2 \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $2$ by $6$ .

$x^{2} = 12$

Step 3

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

$x = \pm \sqrt{12}$

Step 4

Simplify $\pm \sqrt{12}$ .

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Step 4.1

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 4.1.1

Factor $4$ out of $12$ .

$x = \pm \sqrt{4 (3)}$

Step 4.1.2

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

$x = \pm \sqrt{2^{2} \cdot 3}$

Step 4.2

Pull terms out from under the radical.

$x = \pm 2 \sqrt{3}$

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.

$x = 2 \sqrt{3}$

Step 5.2

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

$x = - 2 \sqrt{3}$

Step 5.3

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

$x = 2 \sqrt{3}, - 2 \sqrt{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{3}, - 2 \sqrt{3}$

Decimal Form:

$x = 3.46410161 \dots, - 3.46410161 \dots$