Solve for k k^2-16k+64=0

$k^{2} - 16 k + 64 = 0$

Factor using the perfect square rule.

Rewrite $64$ as $8^{2}$ .

$k^{2} - 16 k + 8^{2} = 0$

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

$16 k = 2 \cdot k \cdot 8$

Rewrite the polynomial.

$k^{2} - 2 \cdot k \cdot 8 + 8^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = k$ and $b = 8$ .

${(k - 8)}^{2} = 0$

Set the $k - 8$ equal to $0$ .

$k - 8 = 0$

Add $8$ to both sides of the equation.

$k = 8$