For this case we must complete squares:
[tex]x ^ 2-16x = 23[/tex]
We add the square of half the coefficient of the term "x",
[tex](\frac {b} {2a}) ^ 2[/tex] on both sides of the equation:
[tex]x ^ 2-16x + (\frac {-16} {2 (1)}) ^ 2 = 23 + (\frac {-16} {2 (1)}) ^ 2\\x ^ 2-16x + (- 8) ^ 2 = 23 + 64[/tex]
According to the perfect square trinomial we have:
[tex](a + b) ^ 2 = a ^2 + 2ab + b ^ 2[/tex]
Rewriting the expression we have:
[tex]a = x\\b = -8\\(x-8) ^ 2 = 23 + 64\\(x-8) ^ 2 = 87[/tex]
ANswer:
[tex](x-8) ^ 2 = 87[/tex]
