Final answer:
To rewrite the quadratic equation 0 = 4x² + 12x - 6 as (x - p)² = q, complete the square by adding and subtracting (3/2)² to get (x + 1.5)² = 3.75, which can also be written as (x - (-1.5))² = 3.75.
Step-by-step explanation:
To rewrite the equation 0 = 4x² + 12x - 6 in the form (x - p)² = q, we first divide each term by 4 to simplify, resulting in 0 = x² + 3x - 1.5. Next, we complete the square for this quadratic equation. To create a perfect square trinomial, we need to add and subtract the square of half the coefficient of 'x', which in this case is (3/2)² or 2.25. Thus, the equation becomes 0 = (x² + 3x + 2.25) - 2.25 - 1.5 or 0 = (x + 1.5)² - 3.75. When we rearrange to isolate the quadratic term, we get (x + 1.5)² = 3.75. Now, simply replace 'x + 1.5' with 'x - (-1.5)' to achieve the desired form: (x - (-1.5))² = 3.75.