The equation - 2x2-8x = 10is rewritten in the form of - 2 (x-p) 2+q = 0. What is the value of q?

q = - 2

Step-by-step explanation:

-2x²-8x = 10 (divide both sides by - 2)

x² + 4x = - 5 (Apply completing the square method)

x² + 4x + (4/2) ² = - 5 + (4/2) ²

x² + 4x + 2² = - 5 + 2² (reduce left hand side using a²+2ab+b² = (a+b) ²)

(x+2) ² = - 5 + 4

(x+2) ² = - 1

(x+2) ² + 1 = 0 (multiply both sides by - 2)

(-2) (x+2) ² + 1 (-2) = 0

-2[x - (-2) ]² + (-2) = 0 - --> compare this with - 2 (x-p) ² + q = 0

We can see that p = 2 and q = - 2