Pre-Algebra Examples

$2 p^{2} = 64$

Step 1

Divide each term in $2 p^{2} = 64$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 p^{2} = 64$ by $2$ .

$\frac{2 p^{2}}{2} = \frac{64}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 p^{2}}{2} = \frac{64}{2}$

Step 1.2.1.2

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

$p^{2} = \frac{64}{2}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $64$ by $2$ .

$p^{2} = 32$

Step 2

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

$p = \pm \sqrt{32}$

Step 3

Simplify $\pm \sqrt{32}$ .

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Step 3.1

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 3.1.1

Factor $16$ out of $32$ .

$p = \pm \sqrt{16 (2)}$

Step 3.1.2

Rewrite $16$ as $4^{2}$ .

$p = \pm \sqrt{4^{2} \cdot 2}$

Step 3.2

Pull terms out from under the radical.

$p = \pm 4 \sqrt{2}$

Step 4

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

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Step 4.1

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

$p = 4 \sqrt{2}$

Step 4.2

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

$p = - 4 \sqrt{2}$

Step 4.3

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

$p = 4 \sqrt{2}, - 4 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$p = 4 \sqrt{2}, - 4 \sqrt{2}$

Decimal Form:

$p = 5.65685424 \dots, - 5.65685424 \dots$