Factor x^2-5x+6.25

$x^{2} - 5 x + 6.25$

Step 1

Rewrite $6.25$ as ${2.5}^{2}$ .

$x^{2} - 5 x + {2.5}^{2}$

Step 2

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

$5 x = 2 \cdot x \cdot 2.5$

Step 3

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 2.5 + {2.5}^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 2.5$ .

${(x - 2.5)}^{2}$