Evaluate (-5/2)^2+5(-5/2)+6

${(- \frac{5}{2})}^{2} + 5 (- \frac{5}{2}) + 6$

Step 1

Simplify each term.

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{5}{2}$ .

${(- 1)}^{2} {(\frac{5}{2})}^{2} + 5 (- \frac{5}{2}) + 6$

Apply the product rule to $\frac{5}{2}$ .

${(- 1)}^{2} \frac{5^{2}}{2^{2}} + 5 (- \frac{5}{2}) + 6$

Raise $- 1$ to the power of $2$ .

$1 \frac{5^{2}}{2^{2}} + 5 (- \frac{5}{2}) + 6$

Multiply $\frac{5^{2}}{2^{2}}$ by $1$ .

$\frac{5^{2}}{2^{2}} + 5 (- \frac{5}{2}) + 6$

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

$\frac{25}{2^{2}} + 5 (- \frac{5}{2}) + 6$

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

$\frac{25}{4} + 5 (- \frac{5}{2}) + 6$

Multiply $5 (- \frac{5}{2})$ .

Multiply $- 1$ by $5$ .

$\frac{25}{4} - 5 (\frac{5}{2}) + 6$

Combine $- 5$ and $\frac{5}{2}$ .

$\frac{25}{4} + \frac{- 5 \cdot 5}{2} + 6$

Multiply $- 5$ by $5$ .

$\frac{25}{4} + \frac{- 25}{2} + 6$

Move the negative in front of the fraction.

$\frac{25}{4} - \frac{25}{2} + 6$

Step 2

Find the common denominator.

Multiply $\frac{25}{2}$ by $\frac{2}{2}$ .

$\frac{25}{4} - (\frac{25}{2} \cdot \frac{2}{2}) + 6$

Multiply $\frac{25}{2}$ by $\frac{2}{2}$ .

$\frac{25}{4} - \frac{25 \cdot 2}{2 \cdot 2} + 6$

Write $6$ as a fraction with denominator $1$ .

$\frac{25}{4} - \frac{25 \cdot 2}{2 \cdot 2} + \frac{6}{1}$

Multiply $\frac{6}{1}$ by $\frac{4}{4}$ .

$\frac{25}{4} - \frac{25 \cdot 2}{2 \cdot 2} + \frac{6}{1} \cdot \frac{4}{4}$

Multiply $\frac{6}{1}$ by $\frac{4}{4}$ .

$\frac{25}{4} - \frac{25 \cdot 2}{2 \cdot 2} + \frac{6 \cdot 4}{4}$

Multiply $2$ by $2$ .

$\frac{25}{4} - \frac{25 \cdot 2}{4} + \frac{6 \cdot 4}{4}$

Step 3

Combine the numerators over the common denominator.

$\frac{25 - 25 \cdot 2 + 6 \cdot 4}{4}$

Step 4

Simplify each term.

Multiply $- 25$ by $2$ .

$\frac{25 - 50 + 6 \cdot 4}{4}$

Multiply $6$ by $4$ .

$\frac{25 - 50 + 24}{4}$

Step 5

Simplify the expression.

Subtract $50$ from $25$ .

$\frac{- 25 + 24}{4}$

Add $- 25$ and $24$ .

$\frac{- 1}{4}$

Move the negative in front of the fraction.

$- \frac{1}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{4}$

Decimal Form:

$- 0.25$

Evaluate (-5/2)^2+5(-5/2)+6

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