Consider the equation: x^2+8x-48=0
A) First, use the "completing the square" process to write this equation in the form (x+D)^2=E and enter your results below.
is equivalent to: x^2+8x-48=0
answer:
To complete the square, we need to add and subtract a constant term to the equation to create a perfect square trinomial.
To do this, we can take half of the coefficient of x and square it. In this case, half of 8 is 4, and 4 squared is 16.
Now, we add and subtract 16 to the equation:
x^2 + 8x - 48 + 16 - 16 = 0
Rearranging the terms, we get:
(x^2 + 8x + 16) - 16 - 48 = 0
This simplifies to:
(x + 4)^2 - 64 = 0
So, the equation x^2 + 8x - 48 = 0 is equivalent to (x + 4)^2 - 64 = 0.