What is the missing constant term in the perfect square that starts with x^2 + 14^x
Mathematics · High School · Tue Nov 03 2020
Answered on
Given:
x^2 + 14x + __
Determine the missing constant to make the perfect square.
Solution:
In order to determine the missing constant, we divide the constant of the 2nd term by 2, and square the quotient, since perfect square solutions are often expressed in the form, a^2 + 2ab+b^2, hence we know that a is x, and in order to get b, we must divide the 2nd term by 2.
= 14/2
= 7
= (7)^2
= 49
Expanded form: x^2 + 14x + 49
Factored form: (x + 7)^2
Final answer:
Expanded form: x^2 + 14x + 49
Factored form: (x + 7)^2