Answer:
[tex]f(x)=(x+8)^{2}-110[/tex]
Step-by-step explanation:
Completing the square is a multi-step process that involved rewriting an equation such that it has a factored term, a coefficient, and a constant. First, group the equation, then add a term such that the grouped part of the equation can be simplified, then balance the equation, finally simplify and factor the equation.
[tex]f(x)=x^{2} +16x - 46\\[/tex]
Group;
[tex]f(x)=(x^{2}+16)-46[/tex]
Add in a term that makes the grouped part of the equation a perfect square, this can be done by dividing the linear term by 2, then balancing the equation;
[tex]f(x)=(x^{2}+16x+64)-46-64[/tex]
Simplify, factor;
[tex]f(x)=(x+8)^{2} - 110[/tex]
