Answer:
[tex]f(x)=(x-5)^{2}+19[/tex]
Step-by-step explanation:
we have
[tex]f(x)=x^{2}-10x+44[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)-44=x^{2}-10x[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]f(x)-44+25=x^{2}-10x+25[/tex]
[tex]f(x)-19=x^{2}-10x+25[/tex]
Rewrite as perfect squares
[tex]f(x)-19=(x-5)^{2}[/tex]
[tex]f(x)=(x-5)^{2}+19[/tex]
