Answer: The given quadratic equation is 2x² - 8x = 10. We can rewrite this equation in the form of 2(x-p)² + q = 0. Comparing the two equations, we can see that:
a = 2 b = -8 c = -10
We know that the vertex form of a quadratic equation is a(x-h)² + k, where (h,k) is the vertex of the parabola. We can convert the given equation to vertex form by completing the square:
2x² - 8x = 10 2(x² - 4x) = 10 2(x² - 4x + 4 - 4) = 10 2((x-2)² - 4) = 10 (x-2)² - 4 = 5 (x-2)² = 9
Therefore, the vertex of the parabola is (2,-4). Since the parabola opens upwards, its minimum value is at the vertex. Thus, q is equal to the minimum value of the parabola, which is -4.
Therefore, the value of q in the equation 2(x-p)² + q = 0 is -4.