Algebra Examples

$f (x) = - 3 x^{5} + 14 x^{4} - 5 x^{2} + 50 x - 1$ at $x = 5$

Step 1

Replace the variable $x$ with $5$ in the expression.

$f (5) = - 3 {(5)}^{5} + 14 {(5)}^{4} - 5 {(5)}^{2} + 50 (5) - 1$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Raise $5$ to the power of $5$ .

$f (5) = - 3 \cdot 3125 + 14 {(5)}^{4} - 5 {(5)}^{2} + 50 (5) - 1$

Step 2.1.2

Multiply $- 3$ by $3125$ .

$f (5) = - 9375 + 14 {(5)}^{4} - 5 {(5)}^{2} + 50 (5) - 1$

Step 2.1.3

Raise $5$ to the power of $4$ .

$f (5) = - 9375 + 14 \cdot 625 - 5 {(5)}^{2} + 50 (5) - 1$

Step 2.1.4

Multiply $14$ by $625$ .

$f (5) = - 9375 + 8750 - 5 {(5)}^{2} + 50 (5) - 1$

Step 2.1.5

Raise $5$ to the power of $2$ .

$f (5) = - 9375 + 8750 - 5 \cdot 25 + 50 (5) - 1$

Step 2.1.6

Multiply $- 5$ by $25$ .

$f (5) = - 9375 + 8750 - 125 + 50 (5) - 1$

Step 2.1.7

Multiply $50$ by $5$ .

$f (5) = - 9375 + 8750 - 125 + 250 - 1$

Step 2.2

Simplify by adding and subtracting.

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Step 2.2.1

Add $- 9375$ and $8750$ .

$f (5) = - 625 - 125 + 250 - 1$

Step 2.2.2

Subtract $125$ from $- 625$ .

$f (5) = - 750 + 250 - 1$

Step 2.2.3

Add $- 750$ and $250$ .

$f (5) = - 500 - 1$

Step 2.2.4

Subtract $1$ from $- 500$ .

$f (5) = - 501$

Step 2.3

The final answer is $- 501$ .

$- 501$

Step 3