Pre-Algebra Examples

${(p - 2)}^{2} = 5$

Step 1

Simplify ${(p - 2)}^{2}$ .

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Step 1.1

Rewrite ${(p - 2)}^{2}$ as $(p - 2) (p - 2)$ .

$(p - 2) (p - 2) = 5$

Step 1.2

Expand $(p - 2) (p - 2)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$p (p - 2) - 2 (p - 2) = 5$

Step 1.2.2

Apply the distributive property.

$p \cdot p + p \cdot - 2 - 2 (p - 2) = 5$

Step 1.2.3

Apply the distributive property.

$p \cdot p + p \cdot - 2 - 2 p - 2 \cdot - 2 = 5$

$p \cdot p + p \cdot - 2 - 2 p - 2 \cdot - 2 = 5$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $p$ by $p$ .

$p^{2} + p \cdot - 2 - 2 p - 2 \cdot - 2 = 5$

Step 1.3.1.2

Move $- 2$ to the left of $p$ .

$p^{2} - 2 \cdot p - 2 p - 2 \cdot - 2 = 5$

Step 1.3.1.3

Multiply $- 2$ by $- 2$ .

$p^{2} - 2 p - 2 p + 4 = 5$

$p^{2} - 2 p - 2 p + 4 = 5$

Step 1.3.2

Subtract $2 p$ from $- 2 p$ .

$p^{2} - 4 p + 4 = 5$

$p^{2} - 4 p + 4 = 5$

$p^{2} - 4 p + 4 = 5$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$p = 2 - \sqrt{5}, 2 + \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$p = 2 - \sqrt{5}, 2 + \sqrt{5}$

Decimal Form:

$p = - 0.23606797 \dots, 4.23606797 \dots$

Step 4

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$