Consider the equation: x^2+6x+8=0
A) First, use the "completing the square" process to write this equation in the form (x+D)=E and enter your results below.
is equivalent to: x^2+6x+8=0
To complete the square for the equation x^2+6x+8=0, we want to rewrite the equation in the form (x+D)^2 = E.
First, we take half of the coefficient of x (which is 6) and square it to get (6/2)^2 = 9. We add this value to both sides of the equation:
x^2 + 6x + 9 + 8 = 9
Now, we can rewrite the left side as the square of a binomial:
(x + 3)^2 = 9
Thus, the equation x^2+6x+8=0 is equivalent to (x+3)^2 = 9.