Precalculus Examples

$2000 = - 14000 {(0 + 15)}^{- \frac{3}{2}} + c$

Step 1

Rewrite the equation as $- 14000 {(0 + 15)}^{- \frac{3}{2}} + c = 2000$ .

$- 14000 {(0 + 15)}^{- \frac{3}{2}} + c = 2000$

Step 2

Simplify $- 14000 {(0 + 15)}^{- \frac{3}{2}} + c$ .

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Step 2.1

Add $0$ and $15$ .

$- 14000 \cdot 15^{- \frac{3}{2}} + c = 2000$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- 14000 \cdot \frac{1}{15^{\frac{3}{2}}} + c = 2000$

Step 2.2.2

Combine $- 14000$ and $\frac{1}{15^{\frac{3}{2}}}$ .

$\frac{- 14000}{15^{\frac{3}{2}}} + c = 2000$

Step 2.2.3

Move the negative in front of the fraction.

$- \frac{14000}{15^{\frac{3}{2}}} + c = 2000$

Step 3

Add $\frac{14000}{15^{\frac{3}{2}}}$ to both sides of the equation.

$c = 2000 + \frac{14000}{15^{\frac{3}{2}}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$c = 2000 + \frac{14000}{15^{\frac{3}{2}}}$

Decimal Form:

$c = 2240.98563043 \dots$