Solve for k k^2+5k+25/4=0

$k^{2} + 5 k + \frac{25}{4} = 0$

Factor using the perfect square rule.

Rewrite $25$ as $5^{2}$ .

$k^{2} + 5 k + \frac{5^{2}}{4} = 0$

Rewrite $4$ as $2^{2}$ .

$k^{2} + 5 k + \frac{5^{2}}{2^{2}} = 0$

Rewrite $\frac{5^{2}}{2^{2}}$ as ${(\frac{5}{2})}^{2}$ .

$k^{2} + 5 k + {(\frac{5}{2})}^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$5 k = 2 \cdot k \cdot \frac{5}{2}$

Rewrite the polynomial.

$k^{2} + 2 \cdot k \cdot \frac{5}{2} + {(\frac{5}{2})}^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = k$ and $b = \frac{5}{2}$ .

${(k + \frac{5}{2})}^{2} = 0$

Set the $k + \frac{5}{2}$ equal to $0$ .

$k + \frac{5}{2} = 0$

Subtract $\frac{5}{2}$ from both sides of the equation.

$k = - \frac{5}{2}$

The result can be shown in multiple forms.

Exact Form:

$k = - \frac{5}{2}$

Decimal Form:

$k = - 2.5$

Mixed Number Form:

$k = - 2 \frac{1}{2}$