Factor x^2-14x+49

$x^{2} - 14 x + 49$

Rewrite $49$ as $7^{2}$ .

$x^{2} - 14 x + 7^{2}$

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

$14 x = 2 \cdot x \cdot 7$

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 7 + 7^{2}$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 7$ .

${(x - 7)}^{2}$