Final answer:
Completing the square of the quadratic equation 6x^2 + 96x - 13 = -13 involves isolating the quadratic and linear terms, factoring out the coefficient of x^2, and adding a value to create a perfect square trinomial. The intermediate step is in the form (x + a)^2 = b, which for this equation simplifies to (x + 8)^2 = 64.
Step-by-step explanation:
Completing the square is a technique used to solve quadratic equations. For the equation 6x^2 + 96x - 13 = -13, we first want to move the constant term to the right side to isolate the quadratic and linear terms:
6x^2 + 96x = 0
Next, we factor out the coefficient of x^2, which is 6, from the left side:
6(x^2 + 16x) = 0
To complete the square, we need to find a value that, when added to x^2 + 16x, will create a perfect square trinomial. We take the coefficient of x, divide it by 2, and square it: (16/2)^2 = 64. Adding and subtracting 64 inside the parentheses keeps the equation balanced:
6(x^2 + 16x + 64 - 64) = 0
Now, we have:
6((x + 8)^2 - 64) = 0
Finally, we simplify to arrive at the intermediate step in the form (x + a)^2 = b:
(x + 8)^2 = 64