Question
what following value "completes the square" or creates a perfect square trinomial, for x^(2)+6x+_
Answers
Answered by
GPT 3.5
To complete the square and create a perfect square trinomial for the quadratic equation x^2 + 6x + _, we need to find the value that makes it a perfect square.
To do this, we take half of the coefficient of x and square it. The coefficient of x is 6, so we take half of 6 and square it: 6/2 = 3, 3^2 = 9.
Therefore, the value that completes the square and creates a perfect square trinomial is 9.
Hence, the quadratic equation can be written as (x + 3)^2 = x^2 + 6x + 9.
To do this, we take half of the coefficient of x and square it. The coefficient of x is 6, so we take half of 6 and square it: 6/2 = 3, 3^2 = 9.
Therefore, the value that completes the square and creates a perfect square trinomial is 9.
Hence, the quadratic equation can be written as (x + 3)^2 = x^2 + 6x + 9.