For this case we have the following expression:
[tex]x ^ 2-8x = 3[/tex]
We must complete squares.
So:
We divide the middle term between two and we square it:
[tex](\frac {-8} {2}) ^ 2[/tex], then:
[tex]x ^ 2-8x + (\frac {-8} {2}) ^ 2 = 3 + (\frac {-8} {2}) ^ 2\\x ^ 2-8x + (- 4) ^ 2 = 3 + 16[/tex]
We have to, by definition:
[tex](a-b) ^ 2 = a ^ 2-2ab + b ^ 2[/tex]
Then, rewriting:
([tex](x-4) ^ 2 = 19[/tex]
To find the roots, we apply square root on both sides:
[tex]x-4 = \sqrt {19}[/tex]
We have two solutions:
[tex]x_ {1} = \sqrt {19} +4\\x_ {2} = - \sqrt {19} +4[/tex]
Answer:
([tex](x-4) ^ 2 = 19\\x_ {1} = \sqrt {19} +4\\x_ {2} = - \sqrt {19} +4[/tex]
