Pre-Algebra Examples

$2420 = 2000 {(1 + r)}^{2}$

Step 1

Simplify $2000 {(1 + r)}^{2}$ .

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Step 1.1

Rewrite ${(1 + r)}^{2}$ as $(1 + r) (1 + r)$ .

$2420 = 2000 ((1 + r) (1 + r))$

Step 1.2

Expand $(1 + r) (1 + r)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$2420 = 2000 (1 (1 + r) + r (1 + r))$

Step 1.2.2

Apply the distributive property.

$2420 = 2000 (1 \cdot 1 + 1 r + r (1 + r))$

Step 1.2.3

Apply the distributive property.

$2420 = 2000 (1 \cdot 1 + 1 r + r \cdot 1 + r \cdot r)$

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 $1$ by $1$ .

$2420 = 2000 (1 + 1 r + r \cdot 1 + r \cdot r)$

Step 1.3.1.2

Multiply $r$ by $1$ .

$2420 = 2000 (1 + r + r \cdot 1 + r \cdot r)$

Step 1.3.1.3

Multiply $r$ by $1$ .

$2420 = 2000 (1 + r + r + r \cdot r)$

Step 1.3.1.4

Multiply $r$ by $r$ .

$2420 = 2000 (1 + r + r + r^{2})$

Step 1.3.2

Add $r$ and $r$ .

$2420 = 2000 (1 + 2 r + r^{2})$

Step 1.4

Apply the distributive property.

$2420 = 2000 \cdot 1 + 2000 (2 r) + 2000 r^{2}$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $2000$ by $1$ .

$2420 = 2000 + 2000 (2 r) + 2000 r^{2}$

Step 1.5.2

Multiply $2$ by $2000$ .

$2420 = 2000 + 4000 r + 2000 r^{2}$

Step 2

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

$r \approx - 2.0\overline{9}, 0.1$

Step 3