Answer :
# to be added to x² +14x to change it to a perfect square trinomial is
(14/2)² = 7²
= 49
the trinomial is x² + 14x + 49 = (x +7)²
(14/2)² = 7²
= 49
the trinomial is x² + 14x + 49 = (x +7)²
[tex](x+a)^2=x^2+2\cdot x\cdot a+a^2\ \ \ \Rightarrow \ \ \ \ 2\cdot x\cdot a=14x\ \ \ \Leftrightarrow\ \ \ 2a=14\ /:2\\\\a=7\ \ \ \Rightarrow\ \ \ a^2=7^2=49\\\\\ \ \ \Rightarrow\ \ \ a\ perfect\ square\ trinomial=(x+7)^2[/tex]
