Factor x^2-5x+25/4

$x^{2} - 5 x + \frac{25}{4}$

Step 1

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

$x^{2} - 5 x + \frac{5^{2}}{4}$

Step 2

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

$x^{2} - 5 x + \frac{5^{2}}{2^{2}}$

Step 3

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

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

Step 4

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

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

Step 5

Rewrite the polynomial.

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

Step 6

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

${(x - \frac{5}{2})}^{2}$