Question

What number should be added to the expression x2 + 14x to change it into a perfect square trinomial?

Answer 1

$(x+a)^2=x^2+2\cdot x\cdot a+a^2\ \ \ \Rightarrow \ \ \ \ 2\cdot x\cdot a=14x\ \ \ \Leftrightarrow\ \ \ 2a=14\ /:2\\\\a=7\ \ \ \Rightarrow\ \ \ a^2=7^2=49\\\\\ \ \ \Rightarrow\ \ \ a\ perfect\ square\ trinomial=(x+7)^2$

Answer 2

# 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